6533b82ffe1ef96bd1295226
RESEARCH PRODUCT
Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences
Tuomo RossiSanna MönköläJukka Räbinäsubject
ta113crystal structureElectromagneticsDiscretizationApplied Mathematicsta111Mathematical analysisFinite differenceFinite-difference time-domain methodDegrees of freedom (statistics)harmonic Hodge operatordiscrete exterior calculusmesh generationComputational Mathematicssymbols.namesakeDiscrete exterior calculusMaxwell's equationsMaxwell's equationsMesh generationnonuniform time discretizationsymbolsMathematicsdescription
We consider the computationally efficient time integration of Maxwell’s equations using discrete exterior calculus (DEC) as the computational framework. With the theory of DEC, we associate the degrees of freedom of the electric and magnetic fields with primal and dual mesh structures, respectively. We concentrate on mesh constructions that imitate the geometry of the close packing in crystal lattices that is typical of elemental metals and intermetallic compounds. This class of computational grids has not been used previously in electromagnetics. For the simulation of wave propagation driven by time-harmonic source terms, we provide an optimized Hodge operator and a novel time discretization scheme with nonuniform time step size. The numerical experiments show a significant improvement in accuracy and a decrease in computing time compared to simulations with well-known variants of the finite difference time domain method. peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 | SIAM Journal on Scientific Computing |