An illustrative hydraulic fracturing simulation method includes: creating an initial mesh representation of a subterranean formation, …

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell’s equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. We demonstrate the effectiveness of these approaches for a variety of cases.

Code verification is an important step towards establishing the credibility of the results of computational physics codes by assessing whether the underlying numerical methods have been correctly implemented. The discretization of differential, integral, or integro-differential equations necessarily incurs some truncation error, and thus the approximate solutions produced from the discretized equations will incur an associated discretization error. If the solution to the problem is known, a measure of the discretization error may be evaluated directly from the approximate solution. The code may be verified by examining the rate at which the error decreases as the discretization is refined, thereby verifying the observed order of accuracy of the discretization scheme is the expected order of accuracy. Electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. These error sources arise from the use of basis functions to approximate the solution, quadrature to numerically integrate, and planar elements to represent curved surfaces. In this work, we provide approaches to separately measure the numerical errors arising from these different error sources using manufactured solutions. We demonstrate the effectiveness of these approaches for cases with and without coding errors.

In this talk, I provide an overview of my research in surrogate model error estimation and code verification. For the first part of this talk, I present an approach to engineer features that, with machine-learning regression, can accurately predict the error incurred by reduced-order models and other approximations to parameterized systems of nonlinear equations. In the second part of this talk, I discuss novel approaches to code verification for hypersonics, ablation, and electromagnetics. These approaches include manufactured solutions, methods for algebraic terms, nonintrusive manufactured solutions, and methods for integral equations with singularities.

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell’s equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. We demonstrate the effectiveness of these approaches for a variety of cases.

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementation of the magnetic-field integral equation, are frequently used to solve Maxwell’s equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this work, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches for cases with and without coding errors.