cl_IF_QUAD4.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_CL_IF_QUAD4_HPP
#define BELFEM_CL_IF_QUAD4_HPP
 
#include "cl_IF_InterpolationFunctionTemplate.hpp"
 
namespace belfem
{
    namespace fem
    {
//------------------------------------------------------------------------------
 
        template<>
        inline InterpolationOrder
        InterpolationFunctionTemplate<
                GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >
        ::interpolation_order() const
        {
            return InterpolationOrder::LINEAR;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        inline ElementType
        InterpolationFunctionTemplate<
                GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >
        ::element_type() const
        {
            return ElementType::QUAD4;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        inline void
        InterpolationFunctionTemplate<
                GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >
        ::param_coords( Matrix< real > & aXiHat )  const
        {
            aXiHat.set_size( 2, 4 );
 
            aXiHat( 0, 0 ) = -1.000000;
            aXiHat( 1, 0 ) = -1.000000;
 
            aXiHat( 0, 1 ) =  1.000000;
            aXiHat( 1, 1 ) = -1.000000;
 
            aXiHat( 0, 2 ) =  1.000000;
            aXiHat( 1, 2 ) =  1.000000;
 
            aXiHat( 0, 3 ) = -1.000000;
            aXiHat( 1, 3 ) =  1.000000;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        inline void
        InterpolationFunctionTemplate<
                GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >::N(
                const Vector< real > & aXi,
                Matrix< real > & aN  ) const
        {
            const real  xi = aXi( 0 );
            const real eta = aXi( 1 );
 
            aN.set_size( 1, 4 );
 
            aN( 0, 0 ) = ( ( 1.0 - xi ) * ( 1.0 - eta ) ) * 0.25;
            aN( 0, 1 ) = ( ( 1.0 + xi ) * ( 1.0 - eta ) ) * 0.25;
            aN( 0, 2 ) = ( ( 1.0 + xi ) * ( 1.0 + eta ) ) * 0.25;
            aN( 0, 3 ) = ( ( 1.0 - xi ) * ( 1.0 + eta ) ) * 0.25;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        inline void
        InterpolationFunctionTemplate<
                GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >::dNdXi(
                const Vector< real > & aXi,
                Matrix< real > & adNdXi  ) const
        {
            const real  xi = aXi( 0 );
            const real eta = aXi( 1 );
 
            adNdXi.set_size( 2, 4 );
 
            adNdXi( 0, 0 ) =  0.25 * ( eta - 1.0 );
            adNdXi( 1, 0 ) =  0.25 * ( xi - 1.0 );
 
            adNdXi( 0, 1 ) = -0.25 * ( eta - 1.0 );
            adNdXi( 1, 1 ) = -0.25 * ( xi + 1.0 );
 
            adNdXi( 0, 2 ) =  0.25 * ( eta + 1.0 );
            adNdXi( 1, 2 ) =  0.25 * ( xi + 1.0 );
 
            adNdXi( 0, 3 ) = -0.25 * ( eta + 1.0 );
            adNdXi( 1, 3 ) = -0.25 * ( xi - 1.0 );
        }
 
//------------------------------------------------------------------------------
 
        template<>
        inline void
        InterpolationFunctionTemplate<
                GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >::d2NdXi2(
                const Vector< real > & aXi,
                Matrix< real > & ad2NdXi2  ) const
        {
            ad2NdXi2.set_size( 3, 4 );
 
            ad2NdXi2( 0, 0 ) =  0.0;
            ad2NdXi2( 1, 0 ) =  0.0;
            ad2NdXi2( 2, 0 ) =  0.25;
 
            ad2NdXi2( 0, 1 ) =  0.0;
            ad2NdXi2( 1, 1 ) =  0.0;
            ad2NdXi2( 2, 1 ) = -0.25;
 
            ad2NdXi2( 0, 2 ) =  0.0;
            ad2NdXi2( 1, 2 ) =  0.0;
            ad2NdXi2( 2, 2 ) =  0.25;
 
            ad2NdXi2( 0, 3 ) =  0.0;
            ad2NdXi2( 1, 3 ) =  0.0;
            ad2NdXi2( 2, 3 ) = -0.25;
        }
 
//------------------------------------------------------------------------------
    }
}
 
#endif //BELFEM_CL_IF_QUAD4_HPP