Vladimir A. Galaktionov

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We study the asymptotic behaviour of classes of global and blow-up solutions of a semilinear parabolic equation of Cahn-Hilliard type u t = −∆(∆u + |u| p−1 u) in R N × R + , p > 1, with bounded integrable initial data. We show that in some {p, N }-parameter ranges it admits a countable set of blow-up similarity patterns. The most interesting set of blow-up(More)
We study the Cauchy problem in R × R + for one-dimensional 2mth-order, m > 1, semilinear parabolic PDEs of the form (Dx = ∂/∂x) ut = (−1) m+1 D 2m x u + |u| p−1 u, where p > 1, and ut = (−1) m+1 D 2m x u + e u with bounded initial data u 0 (x). Specifically, we are interested in those solutions that blow up at the origin in a finite time T. We show that, in(More)
Increased demand for global illumination, image based-lighting and simplified workflow have pushed raytracing into mainstream. Many rendering and simulation algorithms that were considered strictly offline are becoming more interactive on massively parallel GPUs. Unfortunately, the amount of available memory on modern GPUs is relatively small. Scenes for(More)
We present an efficient algorithm for building an adaptive bounding volume hierarchy (BVH) in linear time on commodity graphics hardware using CUDA. BVHs are widely used as an acceleration data structure to quickly ray trace animated polygonal scenes. We accelerate the construction process with auxillary grids that help us build high quality BVHs with SAH(More)
This paper introduces an efficient and simple algorithm for constructing Multiple Reference (MR) octrees on a GPU in application to Photon Mapping and Irradiance Caching techniques. Although MR-octrees are hierarchical structures, we successfully ignore their hierarchical nature and present an approach with plain construction, compact data layout and(More)