Direct combined-field-only integral equations for PEC Maxwell scattering are derived from vector Helmholtz operators, proven uniquely solvable at all frequencies, regularized to second-kind Fredholm form, and corrected for low-frequency breakdown via charge conservation.
P´ erez-Arancibia, C
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The first high-order kernel regularization is derived for the hypersingular Helmholtz operator in 3D, with a unified error analysis that balances regularization and quadrature errors by tying the smoothing parameter to mesh size.
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Maxwell \`a la Helmholtz: Direct boundary integral equations for 3D scattering by perfect electric conductors via Helmholtz operators
Direct combined-field-only integral equations for PEC Maxwell scattering are derived from vector Helmholtz operators, proven uniquely solvable at all frequencies, regularized to second-kind Fredholm form, and corrected for low-frequency breakdown via charge conservation.
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High-order kernel regularization of singular and hypersingular Helmholtz boundary integral operators
The first high-order kernel regularization is derived for the hypersingular Helmholtz operator in 3D, with a unified error analysis that balances regularization and quadrature errors by tying the smoothing parameter to mesh size.