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Award ID contains: 2208164

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  1. ; (, Journal of Scientific Computing)
    Free, publicly-accessible full text available March 1, 2026
  2. ; ; (, Journal of Computational Physics)
    Free, publicly-accessible full text available February 1, 2026
  3. ; ; ; (, Communications on Applied Mathematics and Computation)
    Free, publicly-accessible full text available November 28, 2025
  4. ; ; (, Journal of Scientific Computing)
    Full Text Available 
  5. ; (, Communications on Applied Mathematics and Computation)
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  6. ; ; ; (, BIT Numerical Mathematics)
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  7. ; ; (, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1)
    Melenk, J.M.; Perugia, I.; Schöberl, J.; Schwab, C (Ed.)
    The matrix valued exponential function can be used for time-stepping numerically stiff discretization, such as the discontinuous Galerkin method but this approach is expensive as the matrix is dense and necessitates global communication. In this paper, we propose a local low-rank approximation to this matrix. The local low-rank construction is motivated by the nature of wave propagation and costs significantly less to apply than full exponentiation. The accuracy of this time stepping method is inherited from the exponential integrator and the local property of it allows parallel implementation. The method is expected to be useful in design and inverse problems where many solves of the PDE are required. We demonstrate the error convergence of the method for the one-dimensional (1D) Maxwell’s equation on a uniform grid. 
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