scholarly journals Towards robust, fast solutions of elliptic equations on complex domains through HHO discretizations and non‐nested multigrid methods

2021 ◽  
Author(s):  
D. A. Di Pietro ◽  
F. Hülsemann ◽  
P. Matalon ◽  
P. Mycek ◽  
U. Rüde ◽  
...  
Keyword(s):  
Elliptic Equations ◽  
Multigrid Methods

scholarly journals Chaotic multigrid methods for the solution of elliptic equations

2019 ◽  
Vol 237 ◽  
pp. 26-36 ◽  
Author(s):  
J. Hawkes ◽  
G. Vaz ◽  
A.B. Phillips ◽  
C.M. Klaij ◽  
S.J. Cox ◽  
...  
Keyword(s):  
Elliptic Equations ◽  
Multigrid Methods

scholarly journals Spectral multigrid methods for elliptic equations

1982 ◽  
Vol 48 (3) ◽  
pp. 485-501 ◽  
Author(s):  
Thomas A Zang ◽  
Yau Shu Wong ◽  
M.Y Hussaini
Keyword(s):  
Elliptic Equations ◽  
Multigrid Methods

Spectral multigrid methods for elliptic equations II

1984 ◽  
Vol 54 (3) ◽  
pp. 489-507 ◽  
Author(s):  
Thomas A Zang ◽  
Yau Shu Wong ◽  
M.Yousuff Hussaini
Keyword(s):  
Elliptic Equations ◽  
Multigrid Methods

scholarly journals Simulation techniques for modified gravity

2018 ◽  
Vol 27 (15) ◽  
pp. 1848003 ◽  
Author(s):  
Claudio Llinares
Keyword(s):  
General Relativity ◽  
Nonlinear Equations ◽  
Modified Gravity ◽  
Elliptic Equations ◽  
Large Fraction ◽  
Multigrid Methods ◽  
Cosmological Simulations ◽  
Static Approximation ◽  
Simulation Techniques ◽  
Original Motivation

The standard paradigm of cosmology assumes General Relativity (GR) is a valid theory for gravity at scales in which it has not been properly tested. Developing novel tests of GR and its alternatives is crucial if we want to give strength to the model or find departures from GR in the data. Since alternatives to GR are usually defined through nonlinear equations, designing new tests for these theories implies a jump in complexity and thus, a need for refining the simulation techniques. We summarize existing techniques for dealing with modified gravity (MG) in the context of cosmological simulations. [Formula: see text]-body codes for MG are usually based on standard gravity codes. We describe the required extensions, classifying the models not according to their original motivation, but by the numerical challenges that must be faced by numericists. MG models usually give rise to elliptic equations, for which multigrid techniques are well suited. Thus, we devote a large fraction of this review to describing this particular technique. Contrary to other reviews on multigrid methods, we focus on the specific techniques that are required to solve MG equations and describe useful tricks. Finally, we describe extensions for going beyond the static approximation and dealing with baryons.

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