On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT) | Zendy

Jacob N. Schroder | Zendy

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On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT)

Author(s) -

Jacob N. Schroder

Publication year - 2018

Publication title -

osti oai (u.s. department of energy office of scientific and technical information)

Language(s) - English

Resource type - Reports

DOI - 10.2172/1438750

Subject(s) - multigrid method , reduction (mathematics) , mathematics , relaxation (psychology) , spacetime , grid , simple (philosophy) , domain (mathematical analysis) , dissipation , advection , sine , time domain , focus (optics) , dirichlet distribution , mathematical analysis , computer science , physics , partial differential equation , geometry , quantum mechanics , computer vision , boundary value problem , psychology , social psychology , philosophy , epistemology , optics

on the domain [0, 1.0] × [0, tf ], with zero Dirichlet conditions in space. The initial condition in time is a sine-hump over the first half of the spatial domain (see Figure 1). Solving even this simple problem scalably with a parallel-in-time method has so far proven elusive [4, 2].1 We will focus on the multigrid reduction in time method (MGRIT) [1], which is equivalent to the earlier parareal method [3], in the specialized two-grid setting with F-relaxation. See [1] for a description of the method and of terms like Fand FCF-relaxation.

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