6533b82dfe1ef96bd129202c
RESEARCH PRODUCT
Generalized wave propagation problems and discrete exterior calculus
Lauri KettunenSanna MönköläJukka RäbinäTuomo Rossisubject
raja-arvotHelmholtz equationDiscretizationWave propagationboundary value problemssähkömagnetismielectromagnetism010103 numerical & computational mathematics02 engineering and technologyalgebra01 natural sciencesdiscrete exterior calculusdifferentiaaligeometriaakustiikka0202 electrical engineering electronic engineering information engineeringApplied mathematicsBoundary value problemkvanttimekaniikkadifferential geometry0101 mathematicsacousticsMathematicsta113Numerical AnalysisConservation lawfinite differenceApplied MathematicsFinite difference020206 networking & telecommunicationsFinite element methodComputational MathematicsDiscrete exterior calculusModeling and SimulationelasticityAnalysisexterior algebradescription
We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulative pollution error can be practically eliminated in the case of harmonic wave problems. The restrictions following from the CFL condition can be bypassed with a local time-stepping scheme. The computational savings are at least one order of magnitude.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-05-01 |