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• W2624822772 abstract "Domain decomposition methods in space applied to Partial Differential Equations (PDEs) expanded considerably thanks to their effectiveness (memory costs, calculation costs, better local conditioned problems) and this related to the development of massively parallel machines. Domain decomposition in space-time brings an extra dimension to this optimization. In this work, we study two different direct time-parallel methods for the resolution of Partial Differential Equations. The first part of this work is devoted to the Tensor-product space-time method introduced by R.E. Lynch, J. R. Rice, and D. H. Thomas in 1963. We analyze it in depth for Euler and Crank-Nicolson schemes in time applied to the heat equation. The method needs all time steps to be different, while accuracy is optimal when they are all equal (in the Euler case). Furthermore, when they are close to each other, the condition number of the linear problems involved becomes very big. We thus give for each scheme an algorithm to compute optimal time steps, and present numerical evidences of the quality of the method. The second part of this work deals with the numerical implementation of the Block method of Amodio and Brugnano presented in 1997 to solve the heat equation with Euler and Crank- Nicolson time schemes and the elasticity equation with Euler and Gear time schemes. Our implementation shows how the method is accurate and scalable." @default.
• W2624822772 created "2017-06-23" @default.
• W2624822772 creator A5064621757 @default.
• W2624822772 date "2013-09-24" @default.
• W2624822772 modified "2023-09-23" @default.
• W2624822772 title "Parallel methods in time and in space" @default.
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• W2624822772 hasPublicationYear "2013" @default.
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