NiHu component library reference

Table of Contents

• Introduction
• Function Space Representations
  • Elements
  • Fields and FieldViews
• Kernel Evaluation
  • Laplace equation
  • Helmholtz equation
  • Linear isotropic elastostatics
• Numerical Integration
  • Specialised singular integrals

Introduction

This page is a reference guide of the NiHu Component Library.

Function Space Representations

Elements

linear	quadratic
NiHu::line_1_elem	NiHu::line_2_elem
NiHu::tria_1_elem	NiHu::tria_2_elem
NiHu::quad_1_elem,NiHu::parallelogram_elem	NiHu::quad_2_elem,NiHu::quad_28_elem

Fields and FieldViews

-NiHu::field_option::constant constant function space view generation option -NiHu::field_option::isoparametric isoparametric function space view generation option -NiHu::constant_view constant function space view generation factory function -NiHu::isoparametric_view isoparametric function space view generation factory function

Kernel Evaluation

Laplace equation

• NiHu::laplace_2d_SLP_kernel
• NiHu::laplace_2d_DLP_kernel
• NiHu::laplace_2d_DLPt_kernel
• NiHu::laplace_2d_HSP_kernel
• NiHu::laplace_3d_SLP_kernel
• NiHu::laplace_3d_DLP_kernel
• NiHu::laplace_3d_DLPt_kernel
• NiHu::laplace_3d_HSP_kernel

Helmholtz equation

• NiHu::helmholtz_2d_SLP_kernel
• NiHu::helmholtz_2d_DLP_kernel
• NiHu::helmholtz_3d_SLP_kernel
• NiHu::helmholtz_3d_DLP_kernel
• NiHu::helmholtz_3d_DLPt_kernel
• NiHu::helmholtz_3d_HSP_kernel

Linear isotropic elastostatics

• NiHu::elastostatics_2d_U_kernel
• NiHu::elastostatics_2d_T_kernel
• NiHu::elastostatics_3d_U_kernel
• NiHu::elastostatics_3d_T_kernel

Numerical Integration

Specialised singular integrals

Singular integrals implemented in library/laplace_2d_singular_integrals.hpp

Collocation singular integrals implemented in library/laplace_2d_singular_collocation_integrals.hpp

		NiHu::line_1_elem	NiHu::line_2_elem
SLP	Constant	NiHu::laplace_2d_SLP_collocation_straight	NiHu::laplace_2d_SLP_collocation_curved
	Linear
	Quadratic
DLP	Constant	zero	NiHu::laplace_2d_DLP_collocation_curved
	Linear
	Quadratic
DLPt	Constant	zero	NiHu::laplace_2d_DLPt_collocation_curved
	Linear
	Quadratic
HSP	Constant	NiHu::laplace_2d_HSP_collocation_straight	NiHu::laplace_2d_HSP_collocation_curved
	Linear
	Quadratic

Double singular integrals implemented in library/laplace_2d_singular_double_integrals.hpp

Galerkin face match

		NiHu::line_1_elem	NiHu::line_2_elem
SLP	Constant	NiHu::laplace_2d_SLP_galerkin_face_constant_line	NiHu::laplace_2d_SLP_galerkin_face_general
	Linear	NiHu::laplace_2d_SLP_galerkin_face_linear_line
	Quadratic	NiHu::laplace_2d_SLP_galerkin_face_general
DLP	Constant	zero	NiHu::laplace_2d_DLP_galerkin_face_general
	Linear
	Quadratic
HSP	Constant	NiHu::laplace_2d_HSP_galerkin_face_constant_line	NiHu::laplace_2d_HSP_galerkin_face_general
	Linear	NiHu::laplace_2d_HSP_galerkin_face_general
	Quadratic

Galerkin edge match

		NiHu::line_1_elem	NiHu::line_2_elem
SLP	Constant	NiHu::laplace_2d_SLP_galerkin_edge_constant_line
	Linear
	Quadratic
DLP	Constant	NiHu::laplace_2d_DLP_galerkin_edge_constant_line
	Linear
	Quadratic
HSP	Constant	NiHu::laplace_2d_HSP_galerkin_edge_general
	Linear
	Quadratic

Singular integrals implemented in library/helmholtz_3d_singular_integrals.hpp

• Collocational integral of the Helmholtz 3D SLP kernel over a constant triangle
• Collocational integral of the Helmholtz 3D HSP kernel over a constant triangle
• Galerkin integral of the Helmholtz 2D SLP kernel over a constant line

Singular integrals implemented in library/elastostatics_singular_integrals.hpp

• Galerkin integral of 2D elastostatics U kernel over a constant line
• Galerkin integral of 2D elastostatics T kernel over a constant line

Singular integrals implemented in library/lenoir_salles_2012.hpp

• Galerkin integral of the Laplace 3D SLP kernel over a constant triangle