On mathematical and numerical modelling of multiphysics wave propagation with polytopal discontinuous Galerkin methods: a review
DOI10.1007/s10013-022-00566-3OpenAlexW4285587527MaRDI QIDQ2081567
Michele Botti, Ilario Mazzieri, Paola Francesca Antonietti
Publication date: 13 October 2022
Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.02311
discontinuous Galerkin methodacousticsporoelasticitystability and convergence analysispolygonal and polyhedral meshes
Linear elasticity with initial stresses (74B10) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Soil and rock mechanics (74L10) Seismology (including tsunami modeling), earthquakes (86A15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Linear constitutive equations for materials with memory (74D05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Finite difference and finite volume methods for ordinary differential equations (65L12) PDEs in connection with mechanics of deformable solids (35Q74) PDEs in connection with geophysics (35Q86)
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Cites Work
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- On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
- Time domain numerical modeling of wave propagation in 2D heterogeneous porous media
- Bubble stabilization of discontinuous Galerkin methods
- \(h\)-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems
- High-order absorbing boundary conditions for anisotropic and convective wave equations
- Absorbing boundaries for wave propagation problems
- Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity
- Numerical treatment of two-dimensional interfaces for acoustic and elastic waves.
- A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model
- Solution of coupled poroelastic/acoustic/elastic wave propagation problems using automatic \(h p\)-adaptivity
- Multigrid algorithms for \(hp\)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes
- Arbitrary high order accurate space-time discontinuous Galerkin finite element schemes on staggered unstructured meshes for linear elasticity
- \(V\)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes
- Models, algorithms and error estimation for computational viscoelasticity
- Finite element approximation of a displacement formulation for time-domain elastoacoustic vibrations.
- Generalized Galerkin approximations of elastic waves with absorbing boundary conditions
- High-order discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes
- A low-order nonconforming method for linear elasticity on general meshes
- A high-order discontinuous Galerkin approach to the elasto-acoustic problem
- Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids
- Polytopic discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures
- An \textit{a priori} error estimate for a temporally discontinuous Galerkin space-time finite element method for linear elasto- and visco-dynamics
- A high-order discontinuous Galerkin method for nonlinear sound waves
- A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form
- Stability analysis of discontinuous Galerkin approximations to the elastodynamics problem
- A Nonconforming High-Order Method for the Biot Problem on General Meshes
- hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
- $hp$-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
- Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains
- The Equivalence of Standard and Mixed Finite Element Methods in Applications to Elasto-Acoustic Interaction
- Parallel Octree-Based Finite Element Method for Large-Scale Earthquake Ground Motion Simulation
- Lagrange Multipliers and Optimality
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Wave Propagation Across Acoustic/Biot’s Media: A Finite-Difference Method
- Numerical modeling of seismic waves by discontinuous spectral element methods
- Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids
- ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements
- A High-Order Discontinuous Galerkin Method for the Poro-elasto-acoustic Problem on Polygonal and Polyhedral Grids
- {h-p-hp}-Multilevel discontinuous Galerkin solution strategies for elliptic operators
- An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids
- High–order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations
- A Polygonal Discontinuous Galerkin Formulation for Contact Mechanics in Fluid-Structure Interaction Problems
- The Finite-Difference Modelling of Earthquake Motions
- Analytical Solution for Waves Propagation in Heterogeneous Acoustic/porous Media Part I: the 2D Case
- $hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes
- hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
- Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity problems
- Discontinuous Galerkin Finite Element Method for the Wave Equation
- Elasto–acoustic and acoustic–acoustic coupling on non‐matching grids
- hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes
