The polynomial Trefftz method for solving backward and inverse source wave problems
DOI10.1016/j.cam.2017.01.036zbMath1366.65088OpenAlexW2593977210MaRDI QIDQ2357428
Publication date: 13 June 2017
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2017.01.036
stabilitynumerical examplecollocationinverse source problemTrefftz methodwave polynomialsbackward wave problemhigher-dimensional wave equationmultiple-scale polynomial Trefftz method
Inverse problems for PDEs (35R30) Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The time-marching method of fundamental solutions for wave equations
- Optimally scaled vector regularization method to solve ill-posed linear problems
- Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions
- A multiple-direction Trefftz method for solving the multi-dimensional wave equation in an arbitrary spatial domain
- Series expansions of solutions of the heat equation in \(n\) dimensions
- Cone of non-linear dynamical system and group preserving schemes
- Three-dimensional wave polynomials
- The decomposition method for forward and backward time-dependent problems
- A Lie-group adaptive differential quadrature method to identify an unknown force in an Euler-Bernoulli beam equation
- Solution of the two-dimensional wave equation by using wave polynomials
- Shooting methods for numerical solutions of exact controllability problems constrained by linear and semilinear wave equations with local distributed controls
- Numerical solution of the Laplacian Cauchy problem by using a better postconditioning collocation Trefftz method
- An equilibrated method of fundamental solutions to choose the best source points for the Laplace equation
- Expansion in series of homogeneous temperature functions of the first and second kinds
- Determination of point wave sources by boundary measurements
- Determination of forces in vibrations of beams and plates by pointwise and line observations
- A Two-Side Equilibration Method to Reduce theCondition Number of an Ill-Posed Linear System
- The usage of wave polynomials in solving direct and inverse problems for two-dimensional wave equation
- Real-time reconstruction of time-varying point sources in a three-dimensional scalar wave equation
- An Analytical Method for Computing the One-Dimensional Backward Wave Problem
- Preserving Constraints of Differential Equations by Numerical Methods Based on Integrating Factors
- Expansions in Terms of Heat Polynomials and Associated Functions
- Estimation of point sources and applications to inverse problems
- Determination of point wave sources by pointwise observations: stability and reconstruction
- Upper and lower estimates in determining point sources in a wave equation
- Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method
- Dirichlet, Neumann, and mixed boundary value problems for the wave equationuxx—uyy=0 for a rectangle
- The Dirichlet problem for the vibrating string equation
- Global uniqueness and stability for an inverse wave source problem for less regular data
This page was built for publication: The polynomial Trefftz method for solving backward and inverse source wave problems
