Browsing University of Waterloo by Author "Hachisuka, Toshiya"
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A Monte Carlo Method for Fluid Simulation
Rioux-Lavoie, Damien; Sugimoto, Ryusuke; Ozdemir, Tumay; Shimada, Naoharu H.; Batty, Christopher; Nowrouzezahrai, Derek; Hachisuka, Toshiya (Association for Computing Machinery, 2022-12)We present a novel Monte Carlo-based fluid simulation approach capable of pointwise and stochastic estimation of fluid motion. Drawing on the Feynman-Kac representation of the vorticity transport equation, we propose a ... -
A Practical Walk-on-Boundary Method for Boundary Value Problems
Sugimoto, Ryusuke; Chen, Terry; Jiang, Yiti; Batty, Christopher; Hachisuka, Toshiya (Association for Computing Machinery, 2023-08)We introduce the walk-on-boundary (WoB) method for solving boundary value problems to computer graphics. WoB is a grid-free Monte Carlo solver for certain classes of second order partial differential equations. A similar ... -
Regression-based Monte Carlo Integration
Salaun, Corentin; Gruson, Adrien; Hua, Binh-Son; Hachisuka, Toshiya; Singh, Gurprit (Association for Computing Machinery, 2022-07)Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating ...