A Meshless Time-Domain Method for Geometric Uncertainty Quantification

Numerical electromagnetic computations must often accommodate random geometric representations while handling biological tissues, and engineered components with manufacturing tolerances. Meshless time-domain radial point interpolation method (RPIM) offers advantages to quantitatively analyze such geometric uncertainties using polynomial chaos expansion (PCE). Formulations for geometric uncertainties may require variations in mesh or node distribution for each analyzed sample, leading to high computational requirement for re-meshing. The proposed geometric stochastic RPIM (G-SRPIM) overcomes this with a single domain model by expressing the shape function matrix of RPIM in a stochastic framework. The uncertainty is quantified in G-SRPIM through a novel way by which its random support domain moment matrices are organized in a block structure, and inverted using Schur's complement and Neumann approximation, exploiting the underlying symmetry. The proposed method is validated by analyzing a parallel plate waveguide with a slit exhibiting random variations, a realistic 3D bio-electromagnetic problem involving a section of human head, and an iris filter with random variations in its iris dimensions. Standard deviation upto 45% of the average inter-node distance is tested without jeopardizing the stability. The accuracy of our approach is compared with Monte-Carlo (MC) simulations on a deterministic RPIM using the Kolmogorov-Smirnov (KS) test. Additionally, results are compared with MC simulation on CST<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\text{\text{®}}}$</tex-math></inline-formula> Studio Suit 2018<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\text{™}}$</tex-math></inline-formula> and stochastic collocation (SC). The proposed method exhibits superior execution time compared to SC and MC-based non-intrusive implementations, underscoring its efficiency and reliability in handling geometric uncertainties in microwave components.