b2element_continuum_integrate.H

//------------------------------------------------------------------------
// b2element_continuum_integrate.H --
//
//     Integration schemes for 1D, 2D, and 3D continuum elements.
//
// written by Thomas Ludwig
//
// Copyright (c) 2007-2013,2016,2017
//     SMR Engineering & Development SA
//     2502 Bienne, Switzerland
//
// All Rights Reserved.  Proprietary source code.  The contents of
// this file may not be disclosed to third parties, copied or
// duplicated in any form, in whole or in part, without the prior
// written permission of SMR.
//
// CONTENTS:
//
// - Several parameter classes for one-dimensional Gauss-Legendre
//   integration, for integration over triangles, and for integration
//   over tetrahedrons.  These classes can be used to implement own
//   integration routines, re-using the tested/verified parameters.
//   These parameter classes are of purely static, that is, they need
//   no constructor nor per-object data.
//
// - A class IS_* for each element shape. Instances of these classes
//   can be configured for different integration schemes and for
//   different integration order/number of points.
//------------------------------------------------------------------------
 
#ifndef __B2ELEMENT_CONTINUUM_INTEGRATE_H__
#define __B2ELEMENT_CONTINUUM_INTEGRATE_H__
 
#include <map>
 
#include "elements/properties/b2solid_mechanics.H"
#include "elements/smr/b2element_continuum_util.H"
#include "utils/b2linear_algebra.H"
 
namespace b2000 {
 
//----------------------------------------------------------------------
// Parameters for 1-dimensional Gauss-Legendre integration.
//----------------------------------------------------------------------
 
class GL_Param_1 {
public:
    static const int n = 1;
    static const int o = 1;
    static const double r[1];
    static const double w[1];
};
 
class GL_Param_2 {
public:
    static const int n = 2;
    static const int o = 3;
    static const double r[2];
    static const double w[2];
};
 
class GL_Param_3 {
public:
    static const int n = 3;
    static const int o = 5;
    static const double r[3];
    static const double w[3];
};
 
class GL_Param_4 {
public:
    static const int n = 4;
    static const int o = 7;
    static const double r[4];
    static const double w[4];
};
 
class GL_Param_5 {
public:
    static const int n = 5;
    static const int o = 9;
    static const double r[5];
    static const double w[5];
};
 
class GL_Param_6 {
public:
    static const int n = 6;
    static const int o = 11;
    static const double r[6];
    static const double w[6];
};
 
class GL_Param_7 {
public:
    static const int n = 7;
    static const int o = 13;
    static const double r[7];
    static const double w[7];
};
 
class GL_Param_8 {
public:
    static const int n = 8;
    static const int o = 15;
    static const double r[8];
    static const double w[8];
};
 
class GL_Param_9 {
public:
    static const int n = 9;
    static const int o = 17;
    static const double r[9];
    static const double w[9];
};
 
class GL_Param_10 {
public:
    static const int n = 10;
    static const int o = 19;
    static const double r[10];
    static const double w[10];
};
 
class GL_Param_11 {
public:
    static const int n = 11;
    static const int o = 21;
    static const double r[11];
    static const double w[11];
};
 
class GL_Param_12 {
public:
    static const int n = 12;
    static const int o = 23;
    static const double r[12];
    static const double w[12];
};
 
class GL_Param_13 {
public:
    static const int n = 13;
    static const int o = 25;
    static const double r[13];
    static const double w[13];
};
 
class GL_Param_14 {
public:
    static const int n = 14;
    static const int o = 27;
    static const double r[14];
    static const double w[14];
};
 
class GL_Param_15 {
public:
    static const int n = 15;
    static const int o = 29;
    static const double r[15];
    static const double w[15];
};
 
class GL_Param_16 {
public:
    static const int n = 16;
    static const int o = 31;
    static const double r[16];
    static const double w[16];
};
 
class GL_Param_17 {
public:
    static const int n = 17;
    static const int o = 33;
    static const double r[17];
    static const double w[17];
};
 
class GL_Param_18 {
public:
    static const int n = 18;
    static const int o = 35;
    static const double r[18];
    static const double w[18];
};
 
class GL_Param_19 {
public:
    static const int n = 19;
    static const int o = 37;
    static const double r[19];
    static const double w[19];
};
 
class GL_Param_20 {
public:
    static const int n = 20;
    static const int o = 39;
    static const double r[20];
    static const double w[20];
};
 
class GL_Param_21 {
public:
    static const int n = 21;
    static const int o = 41;
    static const double r[21];
    static const double w[21];
};
 
class GL_Param_22 {
public:
    static const int n = 22;
    static const int o = 43;
    static const double r[22];
    static const double w[22];
};
 
class GL_Param_23 {
public:
    static const int n = 23;
    static const int o = 45;
    static const double r[23];
    static const double w[23];
};
 
class GL_Param_24 {
public:
    static const int n = 24;
    static const int o = 47;
    static const double r[24];
    static const double w[24];
};
 
class GL_Param_25 {
public:
    static const int n = 25;
    static const int o = 49;
    static const double r[25];
    static const double w[25];
};
 
class GL_Param_26 {
public:
    static const int n = 26;
    static const int o = 51;
    static const double r[26];
    static const double w[26];
};
 
class GL_Param_27 {
public:
    static const int n = 27;
    static const int o = 53;
    static const double r[27];
    static const double w[27];
};
 
class GL_Param_28 {
public:
    static const int n = 28;
    static const int o = 55;
    static const double r[28];
    static const double w[28];
};
 
class GL_Param_29 {
public:
    static const int n = 29;
    static const int o = 57;
    static const double r[29];
    static const double w[29];
};
 
class GL_Param_30 {
public:
    static const int n = 30;
    static const int o = 59;
    static const double r[30];
    static const double w[30];
};
 
class GL_Param_31 {
public:
    static const int n = 31;
    static const int o = 61;
    static const double r[31];
    static const double w[31];
};
 
class GL_Param_32 {
public:
    static const int n = 32;
    static const int o = 63;
    static const double r[32];
    static const double w[32];
};
 
//----------------------------------------------------------------------
// Parameters for 1-dimensional Gauss-Legendre-Lobatto integration.
//----------------------------------------------------------------------
 
class GLL_Param_1 {
public:
    static const int n = 1;
    static const int o = 1;
    static const double r[1];
    static const double w[1];
};
 
class GLL_Param_2 {
public:
    static const int n = 2;
    static const int o = 1;
    static const double r[2];
    static const double w[2];
};
 
class GLL_Param_3 {
public:
    static const int n = 3;
    static const int o = 3;
    static const double r[3];
    static const double w[3];
};
 
class GLL_Param_4 {
public:
    static const int n = 4;
    static const int o = 5;
    static const double r[4];
    static const double w[4];
};
 
class GLL_Param_5 {
public:
    static const int n = 5;
    static const int o = 7;
    static const double r[5];
    static const double w[5];
};
 
class GLL_Param_6 {
public:
    static const int n = 6;
    static const int o = 9;
    static const double r[6];
    static const double w[6];
};
 
class GLL_Param_7 {
public:
    static const int n = 7;
    static const int o = 11;
    static const double r[7];
    static const double w[7];
};
 
class GLL_Param_8 {
public:
    static const int n = 8;
    static const int o = 13;
    static const double r[8];
    static const double w[8];
};
 
class GLL_Param_9 {
public:
    static const int n = 9;
    static const int o = 15;
    static const double r[9];
    static const double w[9];
};
 
class GLL_Param_10 {
public:
    static const int n = 10;
    static const int o = 17;
    static const double r[10];
    static const double w[10];
};
 
class GLL_Param_11 {
public:
    static const int n = 11;
    static const int o = 19;
    static const double r[11];
    static const double w[11];
};
 
class GLL_Param_12 {
public:
    static const int n = 12;
    static const int o = 21;
    static const double r[12];
    static const double w[12];
};
 
class GLL_Param_13 {
public:
    static const int n = 13;
    static const int o = 23;
    static const double r[13];
    static const double w[13];
};
 
class GLL_Param_14 {
public:
    static const int n = 14;
    static const int o = 25;
    static const double r[14];
    static const double w[14];
};
 
class GLL_Param_15 {
public:
    static const int n = 15;
    static const int o = 27;
    static const double r[15];
    static const double w[15];
};
 
class GLL_Param_16 {
public:
    static const int n = 16;
    static const int o = 29;
    static const double r[16];
    static const double w[16];
};
 
class GLL_Param_17 {
public:
    static const int n = 17;
    static const int o = 31;
    static const double r[17];
    static const double w[17];
};
 
class GLL_Param_18 {
public:
    static const int n = 18;
    static const int o = 33;
    static const double r[18];
    static const double w[18];
};
 
class GLL_Param_19 {
public:
    static const int n = 19;
    static const int o = 35;
    static const double r[19];
    static const double w[19];
};
 
class GLL_Param_20 {
public:
    static const int n = 20;
    static const int o = 37;
    static const double r[20];
    static const double w[20];
};
 
class GLL_Param_21 {
public:
    static const int n = 21;
    static const int o = 39;
    static const double r[21];
    static const double w[21];
};
 
class GLL_Param_22 {
public:
    static const int n = 22;
    static const int o = 41;
    static const double r[22];
    static const double w[22];
};
 
class GLL_Param_23 {
public:
    static const int n = 23;
    static const int o = 43;
    static const double r[23];
    static const double w[23];
};
 
class GLL_Param_24 {
public:
    static const int n = 24;
    static const int o = 45;
    static const double r[24];
    static const double w[24];
};
 
class GLL_Param_25 {
public:
    static const int n = 25;
    static const int o = 47;
    static const double r[25];
    static const double w[25];
};
 
class GLL_Param_26 {
public:
    static const int n = 26;
    static const int o = 49;
    static const double r[26];
    static const double w[26];
};
 
class GLL_Param_27 {
public:
    static const int n = 27;
    static const int o = 51;
    static const double r[27];
    static const double w[27];
};
 
class GLL_Param_28 {
public:
    static const int n = 28;
    static const int o = 53;
    static const double r[28];
    static const double w[28];
};
 
class GLL_Param_29 {
public:
    static const int n = 29;
    static const int o = 55;
    static const double r[29];
    static const double w[29];
};
 
class GLL_Param_30 {
public:
    static const int n = 30;
    static const int o = 57;
    static const double r[30];
    static const double w[30];
};
 
class GLL_Param_31 {
public:
    static const int n = 31;
    static const int o = 59;
    static const double r[31];
    static const double w[31];
};
 
class GLL_Param_32 {
public:
    static const int n = 32;
    static const int o = 61;
    static const double r[32];
    static const double w[32];
};
 
//----------------------------------------------------------------------
// Parameters for 1-dimensional Clenshaw-Curtis integration.
//----------------------------------------------------------------------
 
class CC_Param_1 {
public:
    static const int n = 1;
    static const int o = 1;
    static const double r[1];
    static const double w[1];
};
 
class CC_Param_2 {
public:
    static const int n = 2;
    static const int o = 1;
    static const double r[2];
    static const double w[2];
};
 
class CC_Param_3 {
public:
    static const int n = 3;
    static const int o = 3;
    static const double r[3];
    static const double w[3];
};
 
class CC_Param_4 {
public:
    static const int n = 4;
    static const int o = n - 1;
    static const double r[4];
    static const double w[4];
};
 
class CC_Param_5 {
public:
    static const int n = 5;
    static const int o = n - 1;
    static const double r[5];
    static const double w[5];
};
 
class CC_Param_6 {
public:
    static const int n = 6;
    static const int o = n - 1;
    static const double r[6];
    static const double w[6];
};
 
class CC_Param_7 {
public:
    static const int n = 7;
    static const int o = n - 1;
    static const double r[7];
    static const double w[7];
};
 
class CC_Param_8 {
public:
    static const int n = 8;
    static const int o = n - 1;
    static const double r[8];
    static const double w[8];
};
 
class CC_Param_9 {
public:
    static const int n = 9;
    static const int o = n - 1;
    static const double r[9];
    static const double w[9];
};
 
class CC_Param_10 {
public:
    static const int n = 10;
    static const int o = n - 1;
    static const double r[10];
    static const double w[10];
};
 
class CC_Param_11 {
public:
    static const int n = 11;
    static const int o = n - 1;
    static const double r[11];
    static const double w[11];
};
 
class CC_Param_12 {
public:
    static const int n = 12;
    static const int o = n - 1;
    static const double r[12];
    static const double w[12];
};
 
class CC_Param_13 {
public:
    static const int n = 13;
    static const int o = n - 1;
    static const double r[13];
    static const double w[13];
};
 
class CC_Param_14 {
public:
    static const int n = 14;
    static const int o = n - 1;
    static const double r[14];
    static const double w[14];
};
 
class CC_Param_15 {
public:
    static const int n = 15;
    static const int o = n - 1;
    static const double r[15];
    static const double w[15];
};
 
class CC_Param_16 {
public:
    static const int n = 16;
    static const int o = n - 1;
    static const double r[16];
    static const double w[16];
};
 
class CC_Param_17 {
public:
    static const int n = 17;
    static const int o = n - 1;
    static const double r[17];
    static const double w[17];
};
 
class CC_Param_18 {
public:
    static const int n = 18;
    static const int o = n - 1;
    static const double r[18];
    static const double w[18];
};
 
class CC_Param_19 {
public:
    static const int n = 19;
    static const int o = n - 1;
    static const double r[19];
    static const double w[19];
};
 
class CC_Param_20 {
public:
    static const int n = 20;
    static const int o = n - 1;
    static const double r[20];
    static const double w[20];
};
 
class CC_Param_21 {
public:
    static const int n = 21;
    static const int o = n - 1;
    static const double r[21];
    static const double w[21];
};
 
class CC_Param_22 {
public:
    static const int n = 22;
    static const int o = n - 1;
    static const double r[22];
    static const double w[22];
};
 
class CC_Param_23 {
public:
    static const int n = 23;
    static const int o = n - 1;
    static const double r[23];
    static const double w[23];
};
 
class CC_Param_24 {
public:
    static const int n = 24;
    static const int o = n - 1;
    static const double r[24];
    static const double w[24];
};
 
class CC_Param_25 {
public:
    static const int n = 25;
    static const int o = n - 1;
    static const double r[25];
    static const double w[25];
};
 
class CC_Param_26 {
public:
    static const int n = 26;
    static const int o = n - 1;
    static const double r[26];
    static const double w[26];
};
 
class CC_Param_27 {
public:
    static const int n = 27;
    static const int o = n - 1;
    static const double r[27];
    static const double w[27];
};
 
class CC_Param_28 {
public:
    static const int n = 28;
    static const int o = n - 1;
    static const double r[28];
    static const double w[28];
};
 
class CC_Param_29 {
public:
    static const int n = 29;
    static const int o = n - 1;
    static const double r[29];
    static const double w[29];
};
 
class CC_Param_30 {
public:
    static const int n = 30;
    static const int o = n - 1;
    static const double r[30];
    static const double w[30];
};
 
class CC_Param_31 {
public:
    static const int n = 31;
    static const int o = n - 1;
    static const double r[31];
    static const double w[31];
};
 
class CC_Param_32 {
public:
    static const int n = 32;
    static const int o = n - 1;
    static const double r[32];
    static const double w[32];
};
 
class CC_Param_33 {
public:
    static const int n = 33;
    static const int o = n - 1;
    static const double r[33];
    static const double w[33];
};
 
//----------------------------------------------------------------------
// Parameters for integration over triangles.
//----------------------------------------------------------------------
 
class T_Param_1 {
public:
    static const int n = 1;
    static const int o = 1;
    static const double r[1];
    static const double s[1];
    static const double w[1];
};
 
class T_Param_3 {
public:
    static const int n = 3;
    static const int o = 2;
    static const double r[3];
    static const double s[3];
    static const double w[3];
};
 
class T_Param_6 {
public:
    static const int n = 6;
    static const int o = 3;
    static const double r[6];
    static const double s[6];
    static const double w[6];
};
 
class T_Param_7 {
public:
    static const int n = 7;
    static const int o = 5;
    static const double r[7];
    static const double s[7];
    static const double w[7];
};
 
class T_Param_12 {
public:
    static const int n = 12;
    static const int o = 6;
    static const double r[12];
    static const double s[12];
    static const double w[12];
};
 
class T_Param_15 {
public:
    static const int n = 15;
    static const int o = 7;
    static const double r[15];
    static const double s[15];
    static const double w[15];
};
 
class T_Param_16 {
public:
    static const int n = 16;
    static const int o = 8;
    static const double r[16];
    static const double s[16];
    static const double w[16];
};
 
class T_Param_19 {
public:
    static const int n = 19;
    static const int o = 9;
    static const double r[19];
    static const double s[19];
    static const double w[19];
};
 
class T_Param_25 {
public:
    static const int n = 25;
    static const int o = 10;
    static const double r[25];
    static const double s[25];
    static const double w[25];
};
 
class T_Param_28 {
public:
    static const int n = 28;
    static const int o = 11;
    static const double r[28];
    static const double s[28];
    static const double w[28];
};
 
class T_Param_33 {
public:
    static const int n = 33;
    static const int o = 12;
    static const double r[33];
    static const double s[33];
    static const double w[33];
};
 
class T_Param_37 {
public:
    static const int n = 37;
    static const int o = 13;
    static const double r[37];
    static const double s[37];
    static const double w[37];
};
 
class T_Param_42 {
public:
    static const int n = 42;
    static const int o = 14;
    static const double r[42];
    static const double s[42];
    static const double w[42];
};
 
class T_Param_49 {
public:
    static const int n = 49;
    static const int o = 15;
    static const double r[49];
    static const double s[49];
    static const double w[49];
};
 
class T_Param_55 {
public:
    static const int n = 55;
    static const int o = 16;
    static const double r[55];
    static const double s[55];
    static const double w[55];
};
 
class T_Param_60 {
public:
    static const int n = 60;
    static const int o = 17;
    static const double r[60];
    static const double s[60];
    static const double w[60];
};
 
class T_Param_67 {
public:
    static const int n = 67;
    static const int o = 18;
    static const double r[67];
    static const double s[67];
    static const double w[67];
};
 
class T_Param_73 {
public:
    static const int n = 73;
    static const int o = 19;
    static const double r[73];
    static const double s[73];
    static const double w[73];
};
 
class T_Param_79 {
public:
    static const int n = 79;
    static const int o = 20;
    static const double r[79];
    static const double s[79];
    static const double w[79];
};
 
class T_Param_87 {
public:
    static const int n;
    static const int o;
    static const double r[87];
    static const double s[87];
    static const double w[87];
};
 
class T_Param_96 {
public:
    static const int n;
    static const int o;
    static const double r[96];
    static const double s[96];
    static const double w[96];
};
 
class T_Param_103 {
public:
    static const int n;
    static const int o;
    static const double r[103];
    static const double s[103];
    static const double w[103];
};
 
class T_Param_112 {
public:
    static const int n;
    static const int o;
    static const double r[112];
    static const double s[112];
    static const double w[112];
};
 
class T_Param_120 {
public:
    static const int n;
    static const int o;
    static const double r[120];
    static const double s[120];
    static const double w[120];
};
 
class T_Param_130 {
public:
    static const int n;
    static const int o;
    static const double r[130];
    static const double s[130];
    static const double w[130];
};
 
class T_Param_141 {
public:
    static const int n;
    static const int o;
    static const double r[141];
    static const double s[141];
    static const double w[141];
};
 
class T_Param_150 {
public:
    static const int n;
    static const int o;
    static const double r[150];
    static const double s[150];
    static const double w[150];
};
 
class T_Param_159 {
public:
    static const int n;
    static const int o;
    static const double r[159];
    static const double s[159];
    static const double w[159];
};
 
class T_Param_171 {
public:
    static const int n;
    static const int o;
    static const double r[171];
    static const double s[171];
    static const double w[171];
};
 
class T_Param_181 {
public:
    static const int n;
    static const int o;
    static const double r[181];
    static const double s[181];
    static const double w[181];
};
 
class T_Param_193 {
public:
    static const int n;
    static const int o;
    static const double r[193];
    static const double s[193];
    static const double w[193];
};
 
class T_Param_204 {
public:
    static const int n;
    static const int o;
    static const double r[204];
    static const double s[204];
    static const double w[204];
};
 
class T_Param_214 {
public:
    static const int n;
    static const int o;
    static const double r[214];
    static const double s[214];
    static const double w[214];
};
 
class T_Param_228 {
public:
    static const int n;
    static const int o;
    static const double r[228];
    static const double s[228];
    static const double w[228];
};
 
class T_Param_243 {
public:
    static const int n;
    static const int o;
    static const double r[243];
    static const double s[243];
    static const double w[243];
};
 
class T_Param_252 {
public:
    static const int n;
    static const int o;
    static const double r[252];
    static const double s[252];
    static const double w[252];
};
 
class T_Param_267 {
public:
    static const int n;
    static const int o;
    static const double r[267];
    static const double s[267];
    static const double w[267];
};
 
class T_Param_282 {
public:
    static const int n;
    static const int o;
    static const double r[282];
    static const double s[282];
    static const double w[282];
};
 
class T_Param_295 {
public:
    static const int n;
    static const int o;
    static const double r[295];
    static const double s[295];
    static const double w[295];
};
 
class T_Param_309 {
public:
    static const int n;
    static const int o;
    static const double r[309];
    static const double s[309];
    static const double w[309];
};
 
class T_Param_324 {
public:
    static const int n;
    static const int o;
    static const double r[324];
    static const double s[324];
    static const double w[324];
};
 
class T_Param_339 {
public:
    static const int n;
    static const int o;
    static const double r[339];
    static const double s[339];
    static const double w[339];
};
 
class T_Param_354 {
public:
    static const int n;
    static const int o;
    static const double r[354];
    static const double s[354];
    static const double w[354];
};
 
class T_Param_370 {
public:
    static const int n;
    static const int o;
    static const double r[370];
    static const double s[370];
    static const double w[370];
};
 
class T_Param_385 {
public:
    static const int n;
    static const int o;
    static const double r[385];
    static const double s[385];
    static const double w[385];
};
 
class T_Param_399 {
public:
    static const int n;
    static const int o;
    static const double r[399];
    static const double s[399];
    static const double w[399];
};
 
class T_Param_423 {
public:
    static const int n;
    static const int o;
    static const double r[423];
    static const double s[423];
    static const double w[423];
};
 
class T_Param_435 {
public:
    static const int n;
    static const int o;
    static const double r[435];
    static const double s[435];
    static const double w[435];
};
 
class T_Param_453 {
public:
    static const int n;
    static const int o;
    static const double r[453];
    static const double s[453];
    static const double w[453];
};
 
//----------------------------------------------------------------------
// Parameters for integration over tetrahedrons.
//----------------------------------------------------------------------
 
// 1-point integration scheme for tetrahedrons (up to order 1 precise).
class TE_Param_1 {
public:
    static const int o = 1;
    static const int n = 1;
    static const double r[1];
    static const double s[1];
    static const double t[1];
    static const double w[1];
 
private:
    static const double a1;
};
 
// 4-point integration scheme for tetrahedrons (up to order 2 precise).
class TE_Param_4 {
public:
    static const int o = 2;
    static const int n = 4;
    static const double r[4];
    static const double s[4];
    static const double t[4];
    static const double w[4];
 
private:
    static const double a1;
    static const double a2;
    static const double w1;
};
 
// 5-point integration scheme for tetrahedrons (up to order 3 precise).
class TE_Param_5 {
public:
    static const int o = 3;
    static const int n = 5;
    static const double r[5];
    static const double s[5];
    static const double t[5];
    static const double w[5];
 
private:
    static const double a1;
    static const double a2;
    static const double a3;
    static const double w1;
    static const double w2;
};
 
// 14-point integration scheme for tetrahedrons (up to order 4 precise).
class TE_Param_14 {
public:
    static const int o = 4;
    static const int n = 14;
    static const double r[14];
    static const double s[14];
    static const double t[14];
    static const double w[14];
};
 
// 15-point integration scheme for tetrahedrons (up to order 5 precise).
class TE_Param_15 {
public:
    static const int o = 5;
    static const int n = 15;
    static const double r[15];
    static const double s[15];
    static const double t[15];
    static const double w[15];
};
 
// 24-point integration scheme for tetrahedrons (up to order 6 precise).
class TE_Param_24 {
public:
    static const int o = 6;
    static const int n = 24;
    static const double r[24];
    static const double s[24];
    static const double t[24];
    static const double w[24];
};
 
//----------------------------------------------------------------------
// Parameters for 15-point Irons volume integration scheme (up to
// order 5 precise).
//----------------------------------------------------------------------
 
class Irons_Param_15 {
public:
    static const int o = 5;
    static const int n = 15;
    static const double r[15];
    static const double s[15];
    static const double t[15];
    static const double w[15];
 
    static const double r1;
    static const double w1;
    static const double w2;
    static const double w3;
};
 
//----------------------------------------------------------------------
// Parameters for 9-point volume reduced integration scheme for
// hexahedrons.
//----------------------------------------------------------------------
 
class Hex_Reduced_Param_9 {
public:
    static const int o = 3;
    static const int n = 9;
    static const double r[9];
    static const double s[9];
    static const double t[9];
    static const double w[9];
 
    static const double r1;
    static const double w0;
    static const double w1;
};
 
//----------------------------------------------------------------------
// Point elements.
//----------------------------------------------------------------------
 
class IS_P {
public:
    int get_num() const { return 1; }
 
    void get_point(const int point_index, double& r, double& weight) const {
        assert(point_index == 0);
        r = 0.;
        weight = 1.;
    }
 
    void get_point(const int point_index, Natural_Coor& rst, double& weight) const {
        std::fill(rst.data(), rst.data() + 3, 0.);
        get_point(point_index, rst[0], weight);
    }
};
 
//----------------------------------------------------------------------
// Integration schemes for line elements.
//----------------------------------------------------------------------
 
class IS_L {
public:
    IS_L() : scheme(0), index(0) {}
 
    int get_num_schemes() const;
 
    int get_scheme() const { return scheme; }
 
    void set_scheme(const int scheme);
 
    void set_scheme_name(const std::string& scheme_name);
 
    const char* get_scheme_name() const { return scheme_names[scheme]; }
 
    void set_order(const int order);
 
    int get_max_order() const;
 
    int get_order() const;
 
    void set_num(const int num_);
 
    int get_num() const;
 
    void get_point(const int point_index, double& r, double& weight) const;
 
    void get_point(const int point_index, Natural_Coor& rst, double& weight) const {
        std::fill(rst.data(), rst.data() + 3, 0.);
        get_point(point_index, rst[0], weight);
    }
 
    void init(ElementProperty& property);
 
private:
    typedef struct {
        enum { GL = 0, GLL = 1, CC = 2, EVENLYSPACED = 3 };
    } SCHEME;
 
    static const char* scheme_names[4];
 
    int scheme;
    int index;
 
    static const int gl_nn = 32;
    static const int gl_n[gl_nn];
    static const int gl_o[gl_nn];
    static const double* gl_r[gl_nn];
    static const double* gl_w[gl_nn];
    static const int gll_nn = 32;
    static const int gll_n[gll_nn];
    static const int gll_o[gll_nn];
    static const double* gll_r[gll_nn];
    static const double* gll_w[gll_nn];
    static const int cc_nn = 32;
    static const int cc_n[cc_nn];
    static const int cc_o[cc_nn];
    static const double* cc_r[cc_nn];
    static const double* cc_w[cc_nn];
};
 
//----------------------------------------------------------------------
// Integration schemes for triangular elements.
//----------------------------------------------------------------------
 
class IS_T {
public:
    IS_T() : scheme(0), index(0) {}
 
    int get_num_schemes() const { return 1; }
 
    int get_scheme() const { return scheme; }
 
    void set_scheme(const int scheme);
 
    void set_scheme_name(const std::string& scheme);
 
    const char* get_scheme_name() const { return scheme_names[scheme]; }
 
    void set_order(const int order);
 
    int get_max_order() const;
 
    int get_order() const;
 
    void set_num(const int num_);
 
    int get_num() const;
 
    void get_point(const int point_index, double rst[2], double& weight) const;
 
    void get_point(const int point_index, Natural_Coor& rst, double& weight) const {
        std::fill(rst.data(), rst.data() + 3, 0.);
        get_point(point_index, rst.data(), weight);
    }
 
    void init(ElementProperty& property);
 
private:
    typedef struct {
        enum { P = 0 };
    } SCHEME;
 
    static const char* scheme_names[1];
 
    static const int pt_nn = 50;
    static const int pt_n[pt_nn];
    static const int pt_o[pt_nn];
    static const double* pt_r[pt_nn];
    static const double* pt_s[pt_nn];
    static const double* pt_w[pt_nn];
 
    int scheme;
    int index;
};
 
//----------------------------------------------------------------------
// Integration schemes for quadrilateral elements.
//----------------------------------------------------------------------
 
class IS_Q {
public:
    const IS_L& operator[](const int direction) const { return is_l[direction]; }
 
    IS_L& operator[](const int direction) { return is_l[direction]; }
 
    void set_order(const int order) {
        int o = 0;
        switch (order) {
            case 2:
                o = 1;
                break;
            case 4:
                o = 2;
                break;
            case 6:
                o = 3;
                break;
            case 8:
                o = 4;
                break;
            case 10:
                o = 5;
                break;
            case 12:
                o = 6;
                break;
            default:
                Exception() << THROW;
                break;
        }
        for (int i = 0; i != 2; ++i) { is_l[i].set_order(o); }
    }
 
    int get_order() const { return is_l[0].get_order() + is_l[1].get_order(); }
 
    void set_num(const int num) {
        int n = 0;
        switch (num) {
            case 1:
                n = 1;
                break;
            case 4:
                n = 2;
                break;
            case 9:
                n = 3;
                break;
            case 16:
                n = 4;
                break;
            case 25:
                n = 5;
                break;
            case 36:
                n = 6;
                break;
            case 49:
                n = 7;
                break;
            case 64:
                n = 8;
                break;
            case 81:
                n = 9;
                break;
            case 100:
                n = 10;
                break;
            case 121:
                n = 11;
                break;
            case 144:
                n = 12;
                break;
            case 169:
                n = 13;
                break;
            case 196:
                n = 14;
                break;
            case 225:
                n = 15;
                break;
            case 256:
                n = 16;
                break;
            case 289:
                n = 17;
                break;
            default:
                Exception() << THROW;
                break;
        }
        for (int i = 0; i != 2; ++i) { is_l[i].set_num(n); }
    }
 
    int get_num() const { return is_l[0].get_num() * is_l[1].get_num(); }
 
    void get_point(const int point_index, double rst[2], double& weight) const {
        const int n0 = is_l[0].get_num();
        const int index[2] = {point_index % n0, point_index / n0};
        double w[2] = {};
        for (int i = 0; i != 2; ++i) { is_l[i].get_point(index[i], rst[i], w[i]); }
        weight = w[0] * w[1];
    }
 
    void get_point(const int point_index, Natural_Coor& rst, double& weight) const {
        std::fill(rst.data(), rst.data() + 3, 0.);
        get_point(point_index, rst.data(), weight);
    }
 
    void init(ElementProperty& property);
 
private:
    IS_L is_l[2];
};
 
//----------------------------------------------------------------------
// Integration schemes for tetrahedral elements.
//----------------------------------------------------------------------
 
class IS_TE {
public:
    IS_TE() : scheme(0), order(0) {}
 
    int get_num_schemes() const { return 1; }
 
    int get_scheme() const { return scheme; }
 
    void set_scheme(const int scheme);
 
    void set_scheme_name(const std::string& scheme);
 
    const char* get_scheme_name() const { return scheme_names[scheme]; }
 
    void set_order(const int order);
 
    int get_max_order() const;
 
    int get_order() const;
 
    void set_num(const int num_);
 
    int get_num() const;
 
    void get_point(const int index, double rst[3], double& weight) const;
 
    void get_point(const int index, Natural_Coor& rst, double& weight) const {
        get_point(index, rst.data(), weight);
    }
 
    void init(ElementProperty& property);
 
private:
    typedef struct {
        enum { P = 0 };
    } SCHEME;
 
    static const char* scheme_names[1];
 
    static const int pte_nn = 6;
    static const int pte_n[pte_nn];
    static const double* pte_r[pte_nn];
    static const double* pte_s[pte_nn];
    static const double* pte_t[pte_nn];
    static const double* pte_w[pte_nn];
 
    static const int pt_nn = 7;
    static const int pt_n[pt_nn];
    static const double* pt_r[pt_nn];
    static const double* pt_s[pt_nn];
    static const double* pt_w[pt_nn];
 
    static const int pgl_nn = 7;
    static const int pgl_gn[pgl_nn];
    static const double* pgl_gr[pgl_nn];
    static const double* pgl_gw[pgl_nn];
 
    int scheme;
    int order;
};
 
//----------------------------------------------------------------------
// Integration schemes for prismatic elements.
//----------------------------------------------------------------------
 
class IS_PR {
public:
    IS_T triangle;
    IS_L line;
 
    void set_num(const int num) {
        switch (num) {
            case 2:
                triangle.set_num(1);
                line.set_num(2);
                break;
            case 6:
                triangle.set_num(3);
                line.set_num(2);
                break;
            case 9:
                triangle.set_num(3);
                line.set_num(3);
                break;
            case 21:
                triangle.set_num(7);
                line.set_num(3);
                break;
            default:
                Exception() << THROW;
                break;
        }
    }
 
    int get_num() const { return triangle.get_num() * line.get_num(); }
 
    void get_point(const int point_index, double rst[3], double& weight) const {
        const int n = triangle.get_num();
        double w[2] = {};
        triangle.get_point(point_index % n, rst, w[0]);
        line.get_point(point_index / n, rst[2], w[1]);
        weight = w[0] * w[1];
    }
 
    void get_point(const int point_index, Natural_Coor& rst, double& weight) const {
        get_point(point_index, rst.data(), weight);
    }
 
    void init(ElementProperty& property);
};
 
//----------------------------------------------------------------------
// Integration schemes for hexahedral elements.
//----------------------------------------------------------------------
 
class IS_HE {
public:
    const IS_L& operator[](const int direction) const { return is_l[direction]; }
 
    IS_L& operator[](const int direction) { return is_l[direction]; }
 
    void set_order(const int order) {
        int o = 0;
        switch (order) {
            case 3:
                o = 1;
                break;
            case 6:
                o = 2;
                break;
            case 9:
                o = 3;
                break;
            case 12:
                o = 4;
                break;
            case 15:
                o = 5;
                break;
            default:
                Exception() << THROW;
                break;
        }
        for (int i = 0; i != 3; ++i) { is_l[i].set_order(o); }
    }
 
    int get_order() const {
        return is_l[0].get_order() + is_l[1].get_order() + is_l[2].get_order();
    }
 
    void set_num(const int num) {
        int n = 0;
        switch (num) {
            case 1:
                n = 1;
                break;
            case 8:
                n = 2;
                break;
            case 27:
                n = 3;
                break;
            case 64:
                n = 4;
                break;
            case 125:
                n = 5;
                break;
            default:
                Exception() << THROW;
                break;
        }
        for (int i = 0; i != 3; ++i) { is_l[i].set_num(n); }
    }
 
    int get_num() const { return is_l[0].get_num() * is_l[1].get_num() * is_l[2].get_num(); }
 
    void get_point(const int point_index, double rst[3], double& weight) const {
        const int n0 = is_l[0].get_num();
        const int n1 = is_l[1].get_num();
        const int index[3] = {point_index % n0, (point_index / n0) % n1, point_index / (n0 * n1)};
        double w[3] = {};
        for (int i = 0; i != 3; ++i) { is_l[i].get_point(index[i], rst[i], w[i]); }
        weight = w[0] * w[1] * w[2];
    }
 
    void get_point(const int point_index, Natural_Coor& rst, double& weight) const {
        get_point(point_index, rst.data(), weight);
    }
 
    void init(ElementProperty& property);
 
private:
    IS_L is_l[3];
};
 
}  // namespace b2000
 
#endif /* __B2ELEMENT_CONTINUUM_INTEGRATE_H__ */