A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance

被引：9

作者：

Bauer, Simon ^{[1
]}

Huber, Markus ^{[2
]}

Mohr, Marcus ^{[1
]}

Ruede, Ulrich ^{[3
,4
]}

Wohlmuth, Barbara ^{[2
]}

机构：

[1] Ludwig Maximilians Univ Munchen, Dept Earth & Environm Sci, Munich, Germany

[2] Tech Univ Munich, Inst Numer Math M2, Munich, Germany

[3] FAU Erlangen Nurnberg, Dept Comp Sci 10, Erlangen, Germany

[4] CERFACS, Parallel Algorithms Project, Toulouse, France

来源：

COMPUTATIONAL SCIENCE - ICCS 2018, PT II | 2018年 / 10861卷

关键词：

Two-scale PDE discretization; Massively parallel multigrid; Matrix-free on-the-fly assembly; Large scale geophysical application; HIERARCHICAL HYBRID GRIDS; MANTLE FLOW; PARALLEL; MODELS; SOLVERS;

D O I：

10.1007/978-3-319-93701-4_2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We report on a two-scale approach for efficient matrix-free finite element simulations. The proposed method is based on surrogate element matrices constructed by low-order polynomial approximations. It is applied to a Stokes-type PDE system with variable viscosity as is a key component in mantle convection models. We set the ground for a rigorous performance analysis inspired by the concept of parallel textbook multigrid efficiency and study the weak scaling behavior on SuperMUC, a peta-scale supercomputer system. For a complex geodynamical model, we achieve a parallel efficiency of 95% on up to 47 250 compute cores. Our largest simulation uses a trillion (O(10(12))) degrees of freedom for a global mesh resolution of 1.7 km.

引用

页码：17 / 30

页数：14

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