scholarly journals Efficient Parallel-in-Time Solution of Time-Periodic Problems Using a MultiHarmonic Coarse Grid Correction

2021 ◽  
Vol 43 (1) ◽  
pp. C61-C88
Author(s):  
Iryna Kulchytska-Ruchka ◽  
Sebastian Schöps
Keyword(s):  
Coarse Grid ◽  
Periodic Problems ◽  
Time Solution ◽  
Coarse Grid Correction ◽  
Time Periodic

Time-periodic solutions of symmetric hyperbolic systems

2020 ◽  
Vol 17 (04) ◽  
pp. 707-726
Author(s):  
Masashi Ohnawa ◽  
Masahiro Suzuki
Keyword(s):  
Periodic Solutions ◽  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Unique Existence ◽  
Periodic Problems ◽  
Time Periodic Solutions ◽  
External Forces ◽  
Initial Boundary Value ◽  
Time Periodic

We prove the unique existence of time-periodic solutions to general hyperbolic equations with periodic external forces autonomous or nonautonomous over a domain bounded by two parallel planes, provided that all the characteristics with respect to the direction normal to the planes have the same sign. It is also shown that global-in-time solutions to initial-boundary value problems coincide with the solutions to corresponding time-periodic problems after a finite time. We devote one section to the reformulation of several realistic problems and see our results have wide applicability.

scholarly journals Coarse grid correction by aggregation / disaggregation with application in image reconstruction

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 755-756
Author(s):  
Constantin Popa ◽  
Aurelian Nicola ◽  
Ulrich Rüde
Keyword(s):  
Image Reconstruction ◽  
Coarse Grid ◽  
Coarse Grid Correction

Parallel implicit time-accurate Navier-Stokes computations using coarse grid correction

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 946-951
Author(s):  
Carl B. Jenssen ◽  
Per A. Weinerfelt
Keyword(s):  
Coarse Grid ◽  
Navier Stokes ◽  
Implicit Time ◽  
Coarse Grid Correction

On the Convergence of System-AMG in Reservoir Simulation

SPE Journal ◽  
2018 ◽  
Vol 23 (02) ◽  
pp. 589-597 ◽  
Author(s):  
Sebastian Gries
Keyword(s):  
Linear Systems ◽  
Reservoir Simulation ◽  
Extreme Case ◽  
Coarse Grid ◽  
Algebraic Multigrid ◽  
Volume Balance ◽  
Coarse Grid Correction ◽  
Speed Up ◽  
Level Problem ◽  
Flexible Framework

Summary System-algebraic multigrid (AMG) provides a flexible framework for linear systems in simulation applications that involve various types of physical unknowns. Reservoir-simulation applications, with their driving elliptic pressure unknown, are principally well-suited to exploit System-AMG as a robust and efficient solver method. However, the coarse grid correction must be physically meaningful to speed up the overall convergence. It has been common practice in constrained-pressure-residual (CPR) -type applications to use an approximate pressure/saturation decoupling to fulfill this requirement. Unfortunately, this can have significant effects on the AMG applicability and, thus, is not performed by the dynamic row-sum (DRS) method. This work shows that the pressure/saturation decoupling is not necessary for ensuring an efficient interplay between the coarse grid correction process and the fine-level problem, demonstrating that a comparable influence of the pressure on the different involved partial-differential equations (PDEs) is much more crucial. As an extreme case with respect to the outlined requirement, linear systems from compositional simulations under the volume-balance formulation will be discussed. In these systems, the pressure typically is associated with a volume balance rather than a diffusion process. It will be shown how System-AMG can still be used in such cases.

Coarse grid correction scheme for implicit multiblock Euler calculations

AIAA Journal ◽  
1995 ◽  
Vol 33 (10) ◽  
pp. 1816-1821 ◽  
Author(s):  
Carl B. Jenssen ◽  
Per A. Weinerfelt
Keyword(s):  
Coarse Grid ◽  
Correction Scheme ◽  
Coarse Grid Correction
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