Numerical methods for the hyperbolic Monge-Ampère equation based on the method of characteristics

DOI10.1007/s42985-022-00181-4zbMath1495.35124arXiv2104.11659OpenAlexW4285044175WikidataQ114216356 ScholiaQ114216356MaRDI QIDQ2162609

M. W. M. C. Bertens, M. J. H. Anthonissen, E. M. T. Vugts, Wilbert L. Ijzerman, Jan H. M. ten Thije Boonkkamp

Publication date: 8 August 2022

Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.11659

zbMATH Keywords

one-step methodsmethod of characteristics for two space dimensions

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Second-order nonlinear hyperbolic equations (35L70) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Uses Software

• UNCMND
• pchip

Cites Work

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• Numerical solution of the optimal transportation problem using the Monge-Ampère equation
• Study of the convergence of interpolation processes with splines of even degree
• Smooth local solutions to degenerate hyperbolic Monge-Ampère equations
• Computational complexity of spline interpolation
• Computation of reflector surfaces for two-variable beam shaping in the hyperbolic case
• Reflector design for two-variable beam shaping in the hyperbolic case
• On the global solubility of the Monge-Ampere hyperbolic equations
• The global smooth solutions of Cauchy problems for hyperbolic equation of Monge-Ampere type
• Partial Differential Equations
• An Iterative Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design
• Numerical Analysis
• Optimal Transport

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