89 citations · 171 across the 26 of their papers we have counts for
27 papers
Convergence of the Semi-Discrete WaveHoltz Iteration
Amit Rotem, Olof Runborg, Daniel Appelo
In this paper we prove that for stable semi-discretizations of the wave equation for the WaveHoltz iteration is guaranteed to converge to an approximate solution of the correspondi…
Error Analysis for the Implicit Boundary Integral Method
Yimin Zhong, Kui Ren, Olof Runborg +1
The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provid…
Error estimates for Gaussian beams at a fold caustic
Olivier Lafitte, Olof Runborg
In this work we show an error estimate for a first order Gaussian beam at a fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For the caustic that…
Corrected Trapezoidal Rule-IBIM for linearized Poisson-Boltzmann equation
Federico Izzo, Yimin Zhong, Olof Runborg +1
In this paper, we solve the linearized Poisson-Boltzmann equation, used to model the electric potential of macromolecules in a solvent. We derive a corrected trapezoidal rule with…
Convergence of a class of high order corrected trapezoidal rules
Federico Izzo, Olof Runborg, Richard Tsai
We present convergence theory for corrected quadrature rules on uniform Cartesian grids for functions with a point singularity. We begin by deriving an error estimate for the punct…
Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation
Fortino Garcia, Daniel Appelö, Olof Runborg
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy…