fn_intpoints_gauss_quad8.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_QUAD8_HPP
#define BELFEM_FN_INTPOINTS_GAUSS_QUAD8_HPP
 
#include "typedefs.hpp"
#include "cl_Vector.hpp"
#include "cl_Matrix.hpp"
 
namespace belfem
{
    namespace integration
    {
// ----------------------------------------------------------------------------
 
        // doi.org/10.1016/j.camwa.2015.03.017
        inline void
        gauss_quad8(
                Vector <real> & aWeights,
                Matrix <real> & aPoints )
        {
            aPoints.set_size( 2, 8 ) ;
            aWeights.set_size( 8 ) ;
 
            aPoints( 0, 0 ) =  0.6831300510639732 ;
            aPoints( 1, 0 ) =  0.0000000000000000 ;
 
            aPoints( 0, 1 ) =  -0.6831300510639732 ;
            aPoints( 1, 1 ) =  0.0000000000000000 ;
 
            aPoints( 0, 2 ) =  0.0000000000000000 ;
            aPoints( 1, 2 ) =  0.6831300510639732 ;
 
            aPoints( 0, 3 ) =  0.0000000000000000 ;
            aPoints( 1, 3 ) =  -0.6831300510639732 ;
 
            aPoints( 0, 4 ) =  0.8819171036881969 ;
            aPoints( 1, 4 ) =  0.8819171036881969 ;
 
            aPoints( 0, 5 ) =  0.8819171036881969 ;
            aPoints( 1, 5 ) =  -0.8819171036881969 ;
 
            aPoints( 0, 6 ) =  -0.8819171036881969 ;
            aPoints( 1, 6 ) =  0.8819171036881969 ;
 
            aPoints( 0, 7 ) =  -0.8819171036881969 ;
            aPoints( 1, 7 ) =  -0.8819171036881969 ;
 
            aWeights( 0 ) = 0.8163265306122449 ;
            aWeights( 1 ) = 0.8163265306122449 ;
            aWeights( 2 ) = 0.8163265306122449 ;
            aWeights( 3 ) = 0.8163265306122449 ;
            aWeights( 4 ) = 0.1836734693877551 ;
            aWeights( 5 ) = 0.1836734693877551 ;
            aWeights( 6 ) = 0.1836734693877551 ;
            aWeights( 7 ) = 0.1836734693877551 ;
        }
 
// ----------------------------------------------------------------------------
    } /* namespace integration */
} /* namespace belfem */
 
#endif //BELFEM_FN_INTPOINTS_GAUSS_QUAD8_HPP