A Reduced-Order PCE-Based Time-Domain Method for Large Uncertainties

Evaluation of uncertainty in field values at a defibrillator probe embedded inside human heart muscles helps in improving the EMI/EMC design of the implants and setting the right thresholds for its safe operation in an environment with electromagnetic (EM) interference. Large variations in EM properties such as dielectric constant and conductivity are expected in such problems. In this article, a 3-D reduced stochastic radial point interpolation method (R-SRPIM) is developed for uncertainty quantification (UQ) in bioelectromagnetics. Derivatives of field quantities in Maxwell’s equations are obtained using the radial basis function, and stochasticity in the EM properties within the model space is incorporated into this formulation. The number of terms in the polynomial chaos expansion (PCE) and hence the computational complexity increases with large variations. To make the resulting formulation computationally viable, the sparsity of the stochastic matrix is enforced by utilizing the linearization property of the product of three Hermite polynomials and using singular value decomposition (SVD). The accuracy of the proposed approach is validated using the Kolmogorov–Smirnov (KS) test, with Monte Carlo (MC) simulations and COMSOL multiphysics.