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Uniform preconditioners for problems of positive order
- Source :
- Computers and Mathematics with Applications, 79(12), 3516-3530. Elsevier
- Publication Year :
- 2020
-
Abstract
- Uniform preconditioners for operators of negative order discretized by (dis)continuous piecewise polynomials of any order are constructed from a boundedly invertible operator of opposite order discretized by continuous piecewise linears. Besides the cost of the application of the latter discretized operator, the other cost of the preconditioner scales linearly with the number of mesh cells. Compared to earlier proposals, the preconditioner has the following advantages: It does not require the inverse of a non-diagonal matrix; it applies without any mildly grading assumption on the mesh; and it does not require a barycentric refinement of the mesh underlying the trial space.
- Subjects :
- Discretization
Preconditioner
MathematicsofComputing_NUMERICALANALYSIS
Inverse
010103 numerical & computational mathematics
Numerical Analysis (math.NA)
Barycentric coordinate system
65F08, 65N38, 65N30, 45EXX
01 natural sciences
law.invention
Mathematics::Numerical Analysis
010101 applied mathematics
Computational Mathematics
Matrix (mathematics)
Operator (computer programming)
Invertible matrix
Computational Theory and Mathematics
law
Modeling and Simulation
Piecewise
FOS: Mathematics
Applied mathematics
Mathematics - Numerical Analysis
0101 mathematics
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 79
- Issue :
- 12
- Database :
- OpenAIRE
- Journal :
- Computers and Mathematics with Applications
- Accession number :
- edsair.doi.dedup.....ee5f43c9b355ee5db43ffec11b9d8fdb