fn_intpoints_gauss_tri4.hpp

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/*
 * BELFEM -- The Berkeley Lab Finite Element Framework
 * Copyright (c) 2026, The Regents of the University of California,
 * through Lawrence Berkeley National Laboratory (subject to receipt of any required
 * approvals from the U.S. Dept. of Energy).  All rights reserved.
 *
 * Developers: Christian Messe, Gregory Giard
 *
 * See the top-level LICENSE file for the complete license and disclaimer.
 */
 
#ifndef BELFEM_FN_INTPOINTS_GAUSS_TRI4_HPP
#define BELFEM_FN_INTPOINTS_GAUSS_TRI4_HPP
 
#include "typedefs.hpp"
#include "cl_Vector.hpp"
#include "cl_Matrix.hpp"
#include "fn_sum.hpp"
 
namespace belfem
{
    namespace integration
    {
// ----------------------------------------------------------------------------
 
        inline void
        gauss_tri4(
                Vector <real> & aWeights,
                Matrix <real> & aPoints )
        {
            // source : 10.1002/nme.1620070316
            aPoints.set_size( 3, 4 );
 
            aPoints( 0, 0 ) = 1.0 / 3.0;
            aPoints( 1, 0 ) = 1.0 / 3.0;
            aPoints( 2, 0 ) = 1.0 / 3.0;
 
            aPoints( 0, 1 ) = 0.6;
            aPoints( 1, 1 ) = 0.2;
            aPoints( 2, 1 ) = 0.2;
 
            aPoints( 0, 2 ) = 0.2;
            aPoints( 1, 2 ) = 0.6;
            aPoints( 2, 2 ) = 0.2;
 
            aPoints( 0, 3 ) = 0.2;
            aPoints( 1, 3 ) = 0.2;
            aPoints( 2, 3 ) = 0.6;
 
            aWeights.set_size( 4 );
 
            aWeights( 0 ) = -27.0 / 96.0;
            aWeights( 1 ) = 25.0 / 96.0;
            aWeights( 2 ) = aWeights( 1 );
            aWeights( 3 ) = aWeights( 1 );
 
            aWeights( 0 ) = 0.0;
            aWeights( 0 ) = 0.5 - sum( aWeights );
 
        }
 
// ----------------------------------------------------------------------------
    } /* namespace integration */
} /* namespace belfem */
 
#endif //BELFEM_FN_INTPOINTS_GAUSS_TRI3_HPP