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Generalised Convolution Quadrature with Runge‐Kutta methods for Acoustic Boundary Elements
Author(s) -
Schanz Martin
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800186
Subject(s) - quadrature (astronomy) , overlap–add method , discretization , convolution (computer science) , mathematics , mathematical analysis , boundary element method , runge–kutta methods , rate of convergence , circular convolution , numerical integration , boundary (topology) , numerical analysis , finite element method , computer science , electronic engineering , physics , fourier transform , fourier analysis , channel (broadcasting) , computer network , machine learning , artificial neural network , fractional fourier transform , thermodynamics , engineering
Abstract In time domain boundary element formulations the convolution in time can be handled by analytical integration or the convolution quadrature method. Here, the generalised convolution quadrature method is applied based on Runge‐Kutta methods. This method allows a variable time step size and the usage of higher order methods in time. The example shows that the variable time step size preserves the convergence order for non‐smooth solutions. The order of convergence is restricted by the low order spatial discretisation.