Convolution Quadrature for Wave Simulations

TL;DR

This paper introduces Convolution Quadrature methods tailored for wave propagation problems, focusing on algorithmic implementation and mathematical foundations for efficient simulation of wave phenomena.

Contribution

It provides a self-contained overview of Convolution Quadrature techniques with emphasis on algorithmic aspects and mathematical tools for wave simulations.

Findings

Develops algorithms for wave-related convolution problems

Provides mathematical background on distributions and calculus

Emphasizes practical implementation for wave simulations

Abstract

These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic aspects. They include introductory material on vector-valued distributions, convolution operators, and Dunford calculus.