Tutorials

Table of Contents

• Basic usage
• Acoustic application examples
• Low level NiHu
• Fast Multipole NiHu
• Customising your own NiHu
• Other

Basic usage

Three steps to build the first NiHu C++ executable

1. Mesh building
2. Function spaces
3. Integral operators and weighted residuals

Two complete examples using the C++ core only

1. Double integral of the Laplace kernel : A Galerkin type singular integral
2. Single integral of the laplace kernel : A collocational type singular integral

Acoustic application examples

These examples build C++ executables that are called from the Matlab frontend

1. Rayleigh integral : Acoustical radiation from a plane surface
2. A Galerkin BEM for the Helmholtz equation : Solving a transparent radiation problem
3. Mitigation of fictitious eigenfrequencies : The CHIEF and Burton-Miller methods
4. Plane wave scattering from an infinite cylinder : An acoustical benchmark case in 2D
5. An indirect collocational Helmholtz BEM example

Low level NiHu

1. Working with elements : How to work with finite elements
2. Working with quadratures : How to work with quadratures

Fast Multipole NiHu

1. Evaluating the Helmholtz kernel using the Fast Multipole Method : Evaluating the 2D Helmholtz kernel using the Fast Multipole Method
2. How to build and work with cluster trees : How to build and work with cluster trees

Customising your own NiHu

1. Defining a custom field : Introduce a new element/field type
2. Customising singular integrals : Specialise a singular integral for a constant triangle
3. Defining a custom kernel : Introduce a new family of PDE into the library

Other

1. Hypersingular integrals : Hypersingular integrals using Guiggiani's method