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)
We present a system for real-time realistic rendering of 3D scenes. Most of available on the market 3d visualization systems lack physical correctness of rendering, especially concerning complex materials and light sources. Our system is aimed to provide the physically correct visualization to the extent possible by modern graphics hardware. It supports(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)