Author: Tianyu Huang
-
A Caveat on Differentiating Time-Domain Wave Boundary Integral Equations
Physicists usually do not worry about the order of integration and differentiation, since in most cases the functions involved are at least C^1-continuous. However, one cannot always take this for granted.
-
Geometric Queries on Closed Implicit Surfaces for Walk on Stars
Walk on stars (WoSt) is currently one of the most advanced Monte Carlo solvers for PDEs. Unfortunately, the lack of reliable geometric query approaches has hindered its applicability to boundaries defined by implicit surfaces. This work proposes a geometric query framework over closed implicit surfaces for WoSt, under the scope of walkin’ Robin. Our key…
-
Hemisphere Sampling or Spherical Sampling: A Small Detail of Importance Sampling the Poisson Kernel in Walk on Boundary
In WoBToolbox, there is a seemingly puzzling step when sampling this term: the author uses uniform hemisphere sampling to generate rays, and this hemisphere is not aligned with the geometric normal of the boundary.
-
Guiding-Based Importance Sampling for Walk on Stars
Walk on stars (WoSt) has shown its power in being applied to Monte Carlo methods for solving partial differential equations, but the sampling techniques in WoSt are not satisfactory, leading to high variance. We propose a guiding-based importance sampling method to reduce the variance of WoSt. Drawing inspiration from path guiding in rendering, we approximate…