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Showing 1 to 4 of 4 for “"Krylov Subspace Spectral Methods"”.
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Krylov Subspace Spectral Methods with Non-homogenous Boundary Conditions
<p>For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their …
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Stability Analysis of Krylov Subspace Spectral Methods for the 1-D Wave Equation in Inhomogeneous Media
<p>Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the …
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Rapid Approximation of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis of Gaussian Node Placement
… rates, which present problems for time-stepping methods. Krylov Subspace Spectral methods, developed by Dr. James Lambers, bridge the gap between explicit and implicit methods for stiff problems by computing each Fouier coefficient from an individualized approximation of the solution operator. …
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Automatic Construction of Scalable Time-Stepping Methods for Stiff PDES
<p>Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. …