Constructs explicit high-order SBP finite difference operators for first-order hyperbolic systems in spherical coordinates with a grid point at the origin to handle 1/r^p singularities while preserving energy stability.
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A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
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High-Order Summation-By-Parts Schemes for First-Order Hyperbolic Systems in Curvilinear Coordinates with Singularities
Constructs explicit high-order SBP finite difference operators for first-order hyperbolic systems in spherical coordinates with a grid point at the origin to handle 1/r^p singularities while preserving energy stability.
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On the Quantisation of Linear Gauge Theories on Lorentzian Manifolds: Maxwell's Theory via Complete Gauge Fixing
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.