Abstract
We establish an abstract space-time DPG framework for the approximation of linear waves in heterogeneous media. The estimates are based on a suitable variational setting in the energy space. The analysis combines the approaches for acoustic waves of Gopalakrishnan–Sepulveda [J. Gopalakrishnan and P. Sepulveda, A space-time DPG method for the wave equation in multiple dimensions, Space-Time Methods. Applications to Partial Differential Equations, Radon Ser. Comput. Appl. Math. 21, Walter de Gruyter, Berlin 2019, 129–154] and Ernesti–Wieners [J. Ernesti and C. Wieners, A space-time discontinuous Petrov–Galerkin method for acoustic waves, Space-Time Methods. Applications to Partial Differential Equations, Radon Ser. Comput. Appl. Math. 21, Walter de Gruyter, Berlin 2019, 99–127] and is based on the abstract definition of traces on the skeleton of the time-space substructuring. The method is evaluated by large-scale parallel computations motivated from applications in seismic imaging, where the computational domain can be restricted substantially to a subset of the full space-time cylinder.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: CRC 1173
Funding statement: We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173. This work was performed on the supercomputer ForHLR funded by the Ministry of Science, Research and the Arts Baden-Württemberg and by the Federal Ministry of Education and Research.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Special Issue Articles on Minimum Residual and Least-Squares Finite Element Methods
- Recent Advances in Least-Squares and Discontinuous Petrov–Galerkin Finite Element Methods
- A Non-conforming Saddle Point Least Squares Approach for an Elliptic Interface Problem
- Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry
- Adaptive Strategies for Transport Equations
- Space-Time Discontinuous Petrov–Galerkin Methods for Linear Wave Equations in Heterogeneous Media
- Superconvergent DPG Methods for Second-Order Elliptic Problems
- The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method
- Fast Integration of DPG Matrices Based on Sum Factorization for all the Energy Spaces
- The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach Spaces
- Camellia: A Rapid Development Framework for Finite Element Solvers
- Alternative Enriched Test Spaces in the DPG Method for Singular Perturbation Problems
- A Newton Div-Curl Least-Squares Finite Element Method for the Elliptic Monge–Ampère Equation
- The Discrete Steklov–Poincaré Operator Using Algebraic Dual Polynomials
- Regular Research Articles
- A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction
- A Second-Order Time-Stepping Scheme for Simulating Ensembles of Parameterized Flow Problems
Articles in the same Issue
- Frontmatter
- Special Issue Articles on Minimum Residual and Least-Squares Finite Element Methods
- Recent Advances in Least-Squares and Discontinuous Petrov–Galerkin Finite Element Methods
- A Non-conforming Saddle Point Least Squares Approach for an Elliptic Interface Problem
- Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry
- Adaptive Strategies for Transport Equations
- Space-Time Discontinuous Petrov–Galerkin Methods for Linear Wave Equations in Heterogeneous Media
- Superconvergent DPG Methods for Second-Order Elliptic Problems
- The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method
- Fast Integration of DPG Matrices Based on Sum Factorization for all the Energy Spaces
- The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach Spaces
- Camellia: A Rapid Development Framework for Finite Element Solvers
- Alternative Enriched Test Spaces in the DPG Method for Singular Perturbation Problems
- A Newton Div-Curl Least-Squares Finite Element Method for the Elliptic Monge–Ampère Equation
- The Discrete Steklov–Poincaré Operator Using Algebraic Dual Polynomials
- Regular Research Articles
- A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction
- A Second-Order Time-Stepping Scheme for Simulating Ensembles of Parameterized Flow Problems