Stochastic Collocation Applications in Computational Electromagnetics

Abstract

The paper reviews the application of deterministic-stochastic models in some areas of computational electromagnetics. Namely, in certain problems there is an uncertainty in the input data set as some properties of a system are partly or entirely unknown. Thus, a simple stochastic collocation (SC) method is used to determine relevant statistics about given responses. The SC approach also provides the assessment of related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. This review paper provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of ground penetrating radar (GPR), human exposure to electromagnetic fields, and buried lines and grounding systems.

An Effective Approach for Uncertain Aerodynamic Analysis of Airfoils via the Polynomial Chaos Expansion

“…Once the PCE model for an airfoil model is determined, the Gaussian quadrature approach can be used to deal with multivariate integrals on the expansion coefficient [29][30][31]. is results in the Galerkin projection [32], the stochastic collocation [33][34][35], and the statistical regression methods [36] in the literature.…”

On the Use of Compound and Extracted Models in Thermal Dosimetry Assessment

“…e anatomically precise models of the complete human body are nowadays available (e.g., [10,11]); however, modeling the detailed human body requires the knowledge of various tissue parameters, while at the same time, significantly burdening the model preparation phase and straining the available computational resources later. e first issue is common to computational analysis of the complex biological system, such as the brain or eye, and is related to the uncertainties of various input parameters that can result in uncertainties in the assessment of the related scenarios [12]. To overcome this problem, the recently used approach is to couple the deterministic model with certain statistical methods, such as stochastic collocation method (SCM) [12] or generalized polynomial chaos (gPC) [13], to name only a few.…”

“…e first issue is common to computational analysis of the complex biological system, such as the brain or eye, and is related to the uncertainties of various input parameters that can result in uncertainties in the assessment of the related scenarios [12]. To overcome this problem, the recently used approach is to couple the deterministic model with certain statistical methods, such as stochastic collocation method (SCM) [12] or generalized polynomial chaos (gPC) [13], to name only a few.…”

“…Although, nowadays, very detailed anatomically correct models, obtained using the MRI, are available, the preparation of such a model can often be a tedious work. e use of a detailed model could lead to long computational time and could raise the memory requirements necessary to run these simulations, preventing the application of optimization techniques or the statistical methods [12,13], where a large number of simulations are often necessary [14]. In addition to this, there are cases when only the particular organ or body parts are of a research interest, or when the initial assessment is considered.…”

Coupling of the Fast Boundary-Domain Integral Method With the Stochastic Collocation Method for Fluid Flow Simulations

“…The reduced computational demands of the algorithm enables us to couple the developed flow simulation algorithm with stochastic modelling of input parameters. In order to assess the influence of input parameters on the simulation results, we employ the stochastic collocation method (SCM, [4], [5]) as a wrapper around the deterministic flow simulation code. In this way, we are able to propagate the uncertainty from input to output parameters.…”