2017/11/14 by William Leeb, Leeb, William, Vladimir Rokhlin +1 · 1 citation
Mathematics · Engineering · Physics and Astronomy · #Numerical methods for differential equations #Electromagnetic Simulation and Numerical Methods #Electromagnetic Scattering and Analysis
paper · pdf · doi:10.48550/arxiv.1711.05354
This paper introduces a fast and numerically stable algorithm for the\nsolution of fourth-order linear boundary value problems on an interval. This\ntype of equation arises in a variety of settings in physics and signal\nprocessing. Our method reformulates the equation as a collection of second-kind\nintegral equations defined on local subdomains. Each such equation can be\nstably discretized and solved. The boundary values of these local solutions are\nmatched by solving a banded linear system. The method of deferred corrections\nis then used to increase the accuracy of the scheme. Deferred corrections\nrequires applying the integral operator to a function on the entire domain, for\nwhich we provide an algorithm with linear cost. We illustrate the performance\nof our method on several numerical examples.\n