cl_IFG_TRI6C.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_IFG_TRI6C_HPP
#define BELFEM_CL_IFG_TRI6C_HPP
 
#include "cl_IF_InterpolationFunctionTemplate.hpp"
 
namespace belfem
{
    namespace fem
    {
//------------------------------------------------------------------------------
 
         
         
//------------------------------------------------------------------------------
 
        template<>
        InterpolationOrder
        InterpolationFunctionTemplate<
                GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >
        ::interpolation_order() const
        {
            return InterpolationOrder::CUBIC;
        }
 
//------------------------------------------------------------------------------
 
        template<>
        ElementType
        InterpolationFunctionTemplate<
                 GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >
        ::element_type() const
        {
            return ElementType::TRI6;
        }
 
//------------------------------------------------------------------------------
 
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >
        ::param_coords( Matrix <real> & aXiHat ) const
        {
            aXiHat.set_size( 2, 2 );
 
            aXiHat( 0, 0 ) =  0.25 ;
            aXiHat( 0, 1 ) =  0.00 ;
            
            aXiHat( 1, 0 ) =  0.75 ;
            aXiHat( 1, 1 ) =  0.00 ;
        }
        
//------------------------------------------------------------------------------
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >::N(
                const Vector <real> & aXi,
                Matrix <real> & aN ) const
        {
            const real   xi = aXi( 0 );
            const real  eta = aXi( 1 );
            const real zeta = 1. - xi - eta ;
            
            aN.set_size( 1, 2 );
            aN( 0, 0 ) = 32./3 * xi * zeta * ( zeta*zeta - xi * xi );
            aN( 0, 1 ) = -aN( 0, 0 );
        }
        
 
//------------------------------------------------------------------------------
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >::dNdXi(
                const Vector <real> & aXi,
                Matrix <real> & adNdXi ) const
        {
            const real   xi = aXi( 0 );
            const real  eta = aXi( 1 );
            const real zeta = 1. - xi - eta ;
            
            real K    = 32./3. ;
    
            real xi2   =  xi*xi ;
            real zeta2 = zeta * zeta ;
            
            adNdXi.set_size( 2, 2 );
            adNdXi( 0, 0 ) = K*((zeta2 - xi2)*(zeta-xi) + 2.*xi*zeta*(eta-1.) );  // dN1/dxi
            adNdXi( 0, 1 ) = K*(xi*(xi2-3.*zeta2));  // dN1/deta
            
            adNdXi( 1, 0 ) = -adNdXi( 0, 0 );
            adNdXi( 1, 1 ) = -adNdXi( 0, 1 );
        }
 
//------------------------------------------------------------------------------
 
 
        template<>
        void
        InterpolationFunctionTemplate<
                GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >::d2NdXi2(
                const Vector <real> & aXi,
                Matrix <real> & ad2NdXi2 ) const
        {
            const real   xi = aXi( 0 );
            const real  eta = aXi( 1 );
            const real zeta = 1. - xi - eta ;
            
            ad2NdXi2.set_size( 3, 2 );
            
            // d²N1/dxi²
            ad2NdXi2( 0, 0 ) =   64./3.*((xi-zeta)*(xi+zeta + 2.*(zeta + xi)) ) ;
            
            // d²N1/deta²
            ad2NdXi2( 1, 0 ) =   64.*xi*zeta;
            
            // d²N1/(dxi*deta)
            ad2NdXi2( 2, 0 ) =   (32./3.)*( (xi-zeta)*(3.*zeta-xi) + 2.*xi*( 2. * xi + zeta));
            
            ad2NdXi2( 0, 1 ) = -ad2NdXi2( 0, 0 ) ;
            ad2NdXi2( 1, 1 ) = -ad2NdXi2( 1, 0 ) ;
            ad2NdXi2( 2, 1 ) = -ad2NdXi2( 2, 0 ) ;
            
        }
 
//------------------------------------------------------------------------------
    }
}
#endif //BELFEM_CL_IFG_TRI6A_HPP