Mean Value Caching for Walk on Spheres

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dc.contributor.authorBakbouk, Ghadaen_US
dc.contributor.authorPeers, Pieteren_US
dc.contributor.editorRitschel, Tobiasen_US
dc.contributor.editorWeidlich, Andreaen_US
dc.date.accessioned2023-06-27T06:41:09Z
dc.date.available2023-06-27T06:41:09Z
dc.date.issued2023
dc.description.abstractWalk on Spheres (WoS) is a grid-free Monte Carlo method for numerically estimating solutions for elliptical partial differential equations (PDE) such as the Laplace and Poisson PDEs. While WoS is efficient for computing a solution value at a single evaluation point, it becomes less efficient when the solution is required over a whole domain or a region of interest. WoS computes a solution for each evaluation point separately, possibly recomputing similar sub-walks multiple times over multiple evaluation points. In this paper, we introduce a novel filtering and caching strategy that leverages the volume mean value property (in contrast to the boundary mean value property that forms the core of WoS). In addition, to improve quality under sparse cache regimes, we describe a weighted mean as well as a non-uniform sampling method. Finally, we show that we can reduce the variance within the cache by recursively applying the volume mean value property on the cached elements.en_US
dc.description.sectionheadersRay Tracing
dc.description.seriesinformationEurographics Symposium on Rendering
dc.identifier.doi10.2312/sr.20231120
dc.identifier.isbn978-3-03868-229-5
dc.identifier.isbn978-3-03868-228-8
dc.identifier.issn1727-3463
dc.identifier.pages1-10
dc.identifier.pages10 pages
dc.identifier.urihttps://doi.org/10.2312/sr.20231120
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/sr20231120
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Computing methodologies -> Shape analysis
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.titleMean Value Caching for Walk on Spheresen_US
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