Space-time adaptive solution of inverse problems with the discrete adjoint method

DOI10.1016/j.jcp.2014.03.042zbMath1349.65409OpenAlexW2020132470MaRDI QIDQ349145

Adrian Sandu, Mihai Alexe

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2014.03.042

zbMATH Keywords

inverse problemsdiscontinuous Galerkindiscrete adjoint methodmesh \(hp\)-refinementRunge-Kutta timestepping

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items

Generalized adjoint consistent treatment of wall boundary conditions for compressible flows, A Posteriori Error Estimates for the Solution of Variational Inverse Problems, POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation, Less is often more: applied inverse problems using \(hp\)-forward models, Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method

Uses Software

• L-BFGS
• deal.ii
• RODAS
• SyFi

Cites Work

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• PDE-constrained optimization with error estimation and control
• Automated solution of differential equations by the finite element method. The FEniCS book
• Adjoint-based \(h\)-\(p\) adaptive discontinuous Galerkin methods for the 2D compressible Euler equations
• Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains
• Automatic differentiation of explicit Runge-Kutta methods for optimal control
• On the limited memory BFGS method for large scale optimization
• Error estimation and adjoint based refinement for an adjoint consistent DG discretisation of the compressible Euler equations
• Local-in-time adjoint-based method for design optimization of unsteady flows
• On the discrete adjoints of adaptive time stepping algorithms
• A posterior error estimation for finite element discretization of parameter identification problems
• Runge-Kutta methods in optimal control and the transformed adjoint system
• Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Adjoint Solutions
• Analysis of Dual Consistency for Discontinuous Galerkin Discretizations of Source Terms
• Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
• Adaptive finite element methods for the solution of inverse problems in optical tomography
• Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation
• A Framework for the Adaptive Finite Element Solution of Large-Scale Inverse Problems
• Applied Shape Optimization for Fluids
• Finite Volume Methods for Hyperbolic Problems
• On the Properties of Runge-Kutta Discrete Adjoints
• Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations
• On the properties of discrete adjoints of numerical methods for the advection equation