Two-dimensional HP-adaptive Algorithm for Continuous Approximations of Material Data Using Space Projection

Gurgul, Piotr; Sieniek, Marcin; Paszyński, Maciej; Madej, Łukasz; Collier, Nathan

doi:10.7494/csci.2013.14.1.97

Cited by 5 publications

(1 citation statement)

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“…In this paper, we present an alternative projection-based interpolation solver that reduces the computational cost to O(N ) in the case of sequential execution and even further to O( N c ) when we use c cores. The projection-based interpolation technique has been successfully used for generating continuous approximations of two-or threedimensional bitmaps, with applications to material science [10,11,12,15] or modeling of the human head [8]. In this paper, we focus on utilizing the Projection-Based Interpolation (PBI) algorithm for solving a sequence of projection problems arising from the Euler scheme used for time discretization of non-stationary problems.…”

Section: Introductionmentioning

confidence: 99%

Application of projection-based interpolation algorithm for non-stationary problem

Woźniak

Paszyński

2016

csci

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In this paper, we present a solver for non-stationary problems using L 2 projection and h-adaptations. The solver utilizes the Euler time integration scheme for time evolution mixed with projection-based interpolation techniques for solving the L 2 projection problem at every time step. The solver is tested on the model problem of a heat transfer in an L-shape domain. We show that our solver delivers linear computational cost at every time step.

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