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- W3048586144 abstract "Abstract A high-order convergent numerical method for solving linear and non-linear parabolic PDEs is presented. The time-stepping is done via an explicit, singly diagonally implicit Runge–Kutta (ESDIRK) method of order 4 or 5, and for the implicit solve, we use the recently developed “Hierarchial Poincaré–Steklov (HPS)” method. The HPS method combines a multidomain spectral collocation discretization technique (a “patching method”) with a nested-dissection type direct solver. In the context under consideration, the elliptic solve required in each time-step involves the same coefficient matrix, which makes the use of a direct solver particularly effective. In this chapter is the first in a two part sequence; the first part describes the methodology, the second part presents numerical experiments." @default.
- W3048586144 created "2020-08-18" @default.
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- W3048586144 date "2020-01-01" @default.
- W3048586144 modified "2023-09-24" @default.
- W3048586144 title "HPS Accelerated Spectral Solvers for Time Dependent Problems: Part I, Algorithms" @default.
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- W3048586144 doi "https://doi.org/10.1007/978-3-030-39647-3_9" @default.
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