High-order vector elements for finite element electromagnetic analysis and subspace method in large-scale eigenvalue problems

2002 ◽  
Vol 85 (7) ◽  
pp. 57-65
Author(s):  
Mitsuo Hano
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
High Order ◽  
Electromagnetic Analysis ◽  
Subspace Method

scholarly journals Efficient exascale discretizations: High-order finite element methods

2021 ◽  
pp. 109434202110208
Author(s):  
Tzanio Kolev ◽  
Paul Fischer ◽  
Misun Min ◽  
Jack Dongarra ◽  
Jed Brown ◽  
...  
Keyword(s):  
Finite Element ◽  
Research And Development ◽  
Finite Element Methods ◽  
Large Scale ◽  
High Efficiency ◽  
High Order ◽  
Computational Time ◽  
Data Movement ◽  
Wide Range ◽  
Matrix Free

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

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