Numerical analysis of an inverse problem for the eikonal equation

DOI10.1007/s00211-011-0386-zzbMath1244.65093OpenAlexW2154277395MaRDI QIDQ644773

Klaus Deckelnick, Charles M. Elliott, Vanessa Styles

Publication date: 7 November 2011

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: http://wrap.warwick.ac.uk/39075/1/WRAP_Elliott_finalVMS-June2011Inverse_eikonal.pdf

zbMATH Keywords

optimal controlinverse problemHamilton-Jacobi equationnumerical exampleserror boundsfinite difference approximationeikonal equationquadratic functionalfast sweeping methodsSoner boundary condition

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Inverse problems for PDEs (35R30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Existence theories for optimal control problems involving partial differential equations (49J20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Discrete approximations in optimal control (49M25) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Hamilton-Jacobi equations (35F21)

Related Items (9)

Finite volume method with the Soner boundary condition for computing the signed distance function on polyhedral meshes ⋮ Bayesian inversion of log-normal eikonal equations ⋮ Tikhonov Regularization within Ensemble Kalman Inversion ⋮ Laplacian regularized eikonal equation with Soner boundary condition on polyhedral meshes ⋮ Solving traveltime tomography with deep learning ⋮ Reconciling Bayesian and Perimeter Regularization for Binary Inversion ⋮ Binary recovery via phase field regularization for first-arrival traveltime tomography ⋮ Mimetic discretization of the eikonal equation with Soner boundary conditions ⋮ Parameter identification problems in the modelling of cell motility

Cites Work

• Unnamed Item
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• Error analysis of numerical schemes for the wave equation in heterogeneous media
• Big ray tracing: Multivalued travel time field computation using viscosity solutions of the eikonal equation
• Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities
• An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals
• Hamilton-Jacobi Equations with State Constraints
• Stable iterative reconstruction algorithm for nonlinear traveltime tomography
• Optimal Control of the Propagation of a Graph in Inhomogeneous Media
• Optimal Control with State-Space Constraint I
• A Simple, Direct Proof of Uniqueness for Solutions of the Hamilton-Jacobi Equations of Eikonal Type
• Numerical Discretization of Boundary Conditions for First Order Hamilton--Jacobi Equations
• Shape-based optimal estimation and design of curve evolution processes with application to plasma etching
• A fast marching level set method for monotonically advancing fronts.

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