manufactured solutions

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 …

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 plays an important role in establishing the credibility of computational simulations by assessing the correctness of …

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.

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing …

The method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the …

Code verification is a necessary step towards establishing credibility in computational physics simulations. It is used to assess the …

The method-of-moments implementation of the electric-field integral equation yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green’s function. In this work, we provide approaches to separately assess the numerical errors arising from the use of basis functions to approximate the solution and the use of quadrature to approximate the integration. Through these approaches, we are able to verify the code and compare the error from different quadrature options.

Code verification is a necessary step towards establishing credibility in computational physics simulations. It is used to assess the correctness of the implementation of the numerical methods within the code, and it is a continuous part of code development. Code verification is typically performed using exact and manufactured solutions. However, exact solutions are often limited, and manufactured solutions generally require the invasive introduction of an artificial forcing term within the source code, such that the code solves a modified problem for which the solution is known. The equations for some physics phenomena, such as non-decomposing ablation, yield infinite analytic solutions, but the boundary conditions may eliminate these possibilities. For such phenomena, however, we can manufacture the terms that comprise the boundary conditions to obtain exact solutions. In this work, we present a nonintrusive method for manufacturing solutions for non-decomposing ablation in two dimensions, which does not require the addition of a source term.