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math.NA2026
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…
math.NA2024
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…
math.NA2024
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…