Parallel \(\mathcal H\)-matrix arithmetics on shared memory systems

DOI10.1007/s00607-004-0102-2zbMath1071.65050OpenAlexW2078704642MaRDI QIDQ556636

Ronald Kriemann

Publication date: 22 June 2005

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-004-0102-2

zbMATH Keywords

finite element methodnumerical examplesboundary element methodparallel algorithmsPoisson equationmatrix inversionmatrix multiplicationmatrix-vector multiplication\(\mathcal H\)-matricesHierarchical matricesshared memory systems

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05) Boundary element methods for boundary value problems involving PDEs (65N38)

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Cites Work

• Unnamed Item
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• Space-filling curves
• Multilevel computations of integral transforms and particle interactions with oscillatory kernels
• Construction and arithmetics of \(\mathcal H\)-matrices
• Introduction to hierarchical matrices with applications.
• Approximation of boundary element matrices
• A sparse \({\mathcal H}\)-matrix arithmetic: General complexity estimates
• Time bounded random access machines
• Integral equations. Theory and numerical treatment
• Efficient partitioning of sequences
• Parallelism in random access machines
• Bounds on Multiprocessing Timing Anomalies
• Depth-First Search and Linear Graph Algorithms