An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients
DOI10.1016/j.camwa.2022.01.010OpenAlexW4210511262MaRDI QIDQ2667958
Publication date: 2 March 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.02511
Helmholtz equationscattering problemadaptive FEMlimiting amplitude principlefront-tracking meshtime-domain wave problem
Wave equation (35L05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)
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Cites Work
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- A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation
- Finite element method for time dependent scattering: nonreflecting boundary condition, adaptivity, and energy decay
- Resolvent estimates at low frequencies and limiting amplitude principle for acoustic propagators
- A mixed formulation and exact controllability approach for the computation of the periodic solutions of the scalar wave equation. I: Controllability problem formulation and related iterative solution
- Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
- Controllability methods for the computation of time-periodic solutions; application to scattering
- Discontinuous Galerkin finite element methods for second order hyperbolic problems
- A posteriori finite element error estimation for second-order hyperbolic problems.
- A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
- Implementation and adaptivity of a space-time finite element method for structural dynamics
- On controllability methods for the Helmholtz equation
- A modified and stable version of a perfectly matched layer technique for the 3-D second order wave equation in time domain with an application to aeroacoustics
- Energy decay and stability of a perfectly matched layer for the wave equation
- Parallel controllability methods for the Helmholtz equation
- Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations
- An improved sweeping domain decomposition preconditioner for the Helmholtz equation
- Controllability method for the Helmholtz equation with higher-order discretizations
- Adaptive Galerkin finite element methods for the wave equation
- Adaptive space-time finite element methods for the wave equation on unbounded domains
- A posteriori L (L2)-error bounds for finite element approximations to the wave equation
- Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
- Numerical Study of an Anisotropic Error Estimator in the $L^2(H^1)$ Norm for the Finite Element Discretization of the Wave Equation
- Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
- Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
- An adaptive finite element method for two-phase Stefan problems in two space dimensions. I. Stability and error estimates
- A Posteriori Error Estimates for Leap-Frog and Cosine Methods for Second Order Evolution Problems
- Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
- Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
- Transient fixed point‐based unstructured mesh adaptation
- A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
- TIME AND SPACE ADAPTIVITY FOR THE SECOND-ORDER WAVE EQUATION
- WaveHoltz: Iterative Solution of the Helmholtz Equation via the Wave Equation
- A Time-Domain Preconditioner for the Helmholtz Equation
- An easily computable error estimator in space and time for the wave equation
- Time and space adaptivity of the wave equation discretized in time by a second-order scheme
- The principle of limiting absorption
- The limiting amplitude principle
- THE PRINCIPLE OF LIMIT AMPLITUDE
- Principles of Limiting Absorption and Limiting Amplitude in Scattering Theory. I. Schrödinger's Equation
- A hybrid numerical asymptotic method for scattering problems
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