Fast computation of elastic and hydrodynamic potentials using approximate approximations
| Autor: | Gunther Schmidt, Flavia Lanzara, Vladimir Maz'ya |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Lame system
Linear elasticity Stokes system High order approximations Computation Gaussian 010103 numerical & computational mathematics Mathematical Analysis Lamé system linear elasticity 01 natural sciences symbols.namesake Operator (computer programming) Matematisk analys Saturation (graph theory) 0101 mathematics Representation (mathematics) Mathematical Physics Physics Algebra and Number Theory 010102 general mathematics Mathematical analysis Order (ring theory) Tensor product symbols Analysis |
| Popis: | We propose fast cubature formulas for the elastic and hydrodynamic potentials based on the approximate approximation of the densities with Gaussian and related functions. For densities with separated representation, we derive a tensor product representation of the integral operator which admits efficient cubature procedures. We obtain high order approximations up to a small saturation error, which is negligible in computations. Results of numerical experiments which show approximation order $$\mathscr {O}(h^{2M})$$ O ( h 2 M ) , $$M=1,2,3,4$$ M = 1 , 2 , 3 , 4 , are provided. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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