38 citations · 224 across the 67 of their papers we have counts for
12 papers · 1 filter
Walk-on-Cubes Monte Carlo Simulation for nonisotropic fractional Laplace, Helmholtz, and Yukawa equations
Antti Rasila, Tommi Sottinen, Yaotong Yuan
We study the nonisotropic fractional analogs of Laplace, Helmholtz and Yukawa equations. We provide a Duffin correspondence for the Yukawa equation and a Feynman--Kac reconstructio…
Laplace--Beltrami Equations and Numerical Conformal Mappings on Surfaces
Harri Hakula, Antti Rasila
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains. In this paper, the conjugate function metho…
Efficient simulation of mixed boundary value problems and conformal mappings
Qiansheng Han, Antti Rasila, Tommi Sottinen
In this paper, we present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular a…
Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence
Xuxin Yang, Antti Rasila, Tommi Sottinen
We show that a constant-potential time-independent Schrödinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With th…
Efficient simulation of Schrödinger equation with piecewise constant positive potential
Xuxin Yang, Antti Rasila, Tommi Sottinen
In this paper we introduce a new method for the simulation of a weak solution of the Schrödinger-type equation where the potential is piecewise constant and positive. The method, c…
Conjugate Function Method and Conformal Mappings in Multiply Connected Domains
Harri Hakula, Tri Quach, Antti Rasila
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method i…