cl_IF_BEAM.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_BEAM_HPP
#define BELFEM_CL_IF_BEAM_HPP
 
 
#include "cl_IF_InterpolationFunctionTemplate.hpp"
 
namespace belfem
{
    namespace fem
    {
//------------------------------------------------------------------------------
 
        template<>
        InterpolationOrder
        InterpolationFunctionTemplate<
                GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >
        ::interpolation_order() const
        {
            return InterpolationOrder::CUBIC;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        ElementType
        InterpolationFunctionTemplate<
                GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >
        ::element_type() const
        {
            return ElementType::LINE2;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >
        ::param_coords( Matrix< real > & aXiHat )  const
        {
            aXiHat.set_size( 1, 2 );
 
            aXiHat( 0, 0 ) = -1.0;
            aXiHat( 0, 1 ) =  1.0;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >::N(
                const Vector< real > & aXi,
                Matrix< real > & aN  ) const
        {
            const real xi = aXi( 0 );
 
            const real a = (xi-1.0);
            const real b = (xi+1.0);
 
            aN.set_size( 1, 4 );
 
            aN( 0, 0 ) = a*a*(xi+2.0);
            aN( 0, 1 ) = a*a*b;
            aN( 0, 2 ) = b*b*(2.0-xi);
            aN( 0, 3 ) = b*b*a;
 
            aN *= 0.25;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >::dNdXi(
                const Vector< real > & aXi,
                Matrix< real > & adNdXi  ) const
        {
            const real xi = aXi( 0 );
            const real xi2 = xi*xi;
 
            adNdXi.set_size( 1, 4 );
            adNdXi( 0, 0 ) =  3.0*(xi2-1.0);
            adNdXi( 0, 1 ) = (3.0*xi-2.0)*xi-1.0;
            adNdXi( 0, 2 ) = 3.0*(1.0-xi2);
            adNdXi( 0, 3 ) = (3.0*xi+2.0)*xi-1.0;
            adNdXi *= 0.25;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >::d2NdXi2(
                const Vector< real > & aXi,
                Matrix< real > & ad2NdXi2  ) const
        {
            const real xi = aXi( 0 );
 
            ad2NdXi2.set_size( 1, 4 );
            ad2NdXi2(0, 0 ) =  3.0*xi;
            ad2NdXi2(0, 1 ) =  3.0*xi-1.0;
            ad2NdXi2(0, 2 ) = -3.0*xi;
            ad2NdXi2(0, 3 ) =  3.0*xi+1.0;
 
            ad2NdXi2*=0.5;
        }
 
//------------------------------------------------------------------------------
    }
}
 
#endif //BELFEM_CL_IF_BEAM_HPP