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Mathematical Sciences Colloquium: Low-Rank Tensor Methods for Vlasov Simulations

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Friday, April 16, 2021 1:00pm to 1:50pm

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Speaker: Professor Wei Guo (Texas Tech )

Abstract:  We present a low-rank tensor approach for solving the Vlasov equation. Among many existing challenges for Vlasov simulations (e.g. multi-scale features, nonlinearity, formation of filamentation structures), the curse of dimensionality and the associated huge computational cost have been a long-standing key obstacle for realistic high-dimensional simulations. In this work, we propose to overcome the curse of dimensionality by dynamically and adaptively exploring a low-rank tensor representation of Vlasov solutions in a general high-dimensional setting. In particular, we develop two different approaches: one is to directly solve the unknown function, and the other is to solve the underlying flow map, aiming to obtain a low-rank approximation with optimal complexity. The performance of both proposed algorithms is benchmarked for standard Vlasov-Poisson/Maxwell test problems.

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