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International Journal for Uncertainty Quantification

Impact factor: 0.967

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2015010170
pages 195-208

UNCERTAINTY QUANTIFICATION FOR MAXWELL'S EQUATIONS USING STOCHASTIC COLLOCATION AND MODEL ORDER REDUCTION

Peter Benner
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
Judith Schneider
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany

ABSTRACT

Modeling and simulation are indispensable for the design process of new semiconductor structures. Difficulties arise from shrinking structure sizes, increasing working frequencies, and uncertainties of materials and geometries. Therefore, we consider the time-harmonic Maxwell's equations for the simulation of a coplanar waveguide with uncertain material parameters. To analyze the uncertainty of the system, we use stochastic collocation with Stroud and sparse grid points. The results are compared to a Monte Carlo simulation. Both methods rely on repetitive runs of a deterministic solver. To accelerate this, we compute a reduced model by means of proper orthogonal decomposition to reduce the computational cost. The Monte Carlo simulation and the stochastic collocation are both applied to the full and the reduced model. All results are compared concerning accuracy and computation time.