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teaching:ft1920:praktikum:start [2019/10/16 15:28] ipa ExpInt: Slides from the introduction |
teaching:ft1920:praktikum:start [2021/03/02 13:28] (current) |
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| ==== Introduction ==== | ==== Introduction ==== | ||
| - | * {{teaching:ft1920:praktikum:files:niesen_and_wright_-_algorithm_919_a_krylov_subspace_algorithm_for_ev.pdf|Niesen, Wright - Algorithm 919: A Krylov Subspace Algorithm for Evaluating the φ-Functions Appearing in Exponential Integrators}} Good introduction, idea of time stepping | + | * {{teaching:ft1920:praktikum:files:niesen_and_wright_-_algorithm_919_a_krylov_subspace_algorithm_for_eva.pdf|Niesen, Wright - Algorithm 919: A Krylov Subspace Algorithm for Evaluating the φ-Functions Appearing in Exponential Integrators}} Good introduction, idea of time stepping |
| ==== Special topics ==== | ==== Special topics ==== | ||
| - | * {{teaching:ft1920:praktikum:files:al-mohy_higham_-_computing_the_action_of_the_matrix_exponential_with_an_application_to_exponential_integrators.pdf| Al-Hohy, Higham - Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators}} computing $e^A B$, computing $e^{tA} B$ over a time intervall | + | * {{teaching:ft1920:praktikum:files:al-mohy_higham_-_computing_the_action_of_the_matrix_exponential_with_an_application_to_exponential_integrators.pdf| Al-Hohy, Higham - Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators}} computing $e^A B$, computing $e^{tA} B$ over a time intervall |
| + | * {{hochbruck_and_lubich_-_1997_-_on_krylov_subspace_approximations_to_the_matrix_ex.pdf| Hochbruck, Lubich - On Krylov subspace approximations to the Matrix Exponential Operator}} Error bounds | ||
| + | * {{teaching:ft1920:praktikum:files:saad_-_analysis_of_some_krylov_subspace_approximations_to.pdf|Saad - Analysis of some Krylov Subspace Approximations to the Matrix Exponential Operator}} Error bounds | ||
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| * {{teaching:ft1920:praktikum:files:moler2003_-_nineteen_dubious_ways_to_compute_the_exponential_of_a_matrix_twenty_five_years_later.pdf|Moler, Van Loan - Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later}} this paper is the definitive guide on how to calculate the exponential of a matrix | * {{teaching:ft1920:praktikum:files:moler2003_-_nineteen_dubious_ways_to_compute_the_exponential_of_a_matrix_twenty_five_years_later.pdf|Moler, Van Loan - Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later}} this paper is the definitive guide on how to calculate the exponential of a matrix | ||
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| + | ==== Application of Exponential Integrators ==== | ||
| + | * {{teaching:ft1920:praktikum:files:hochbruck_and_ostermann_-_exponential_integrators.pdf|Hochbruck, Ostermann - Exponential integrators}} application to stiff problems | ||
| ==== Software ==== | ==== Software ==== | ||
| * {{teaching:ft1920:praktikum:files:sidje_-_expokit_a_software_package_for_computing_matrix_exponentials.pdf| Sidje - Expokit: A Software Package for ComputingMatrix Exponentials}} Expokit is a Fortran/Matlab implementation of exponential integrators, the paper contains a lot of useful details on implementing exponential integrators. | * {{teaching:ft1920:praktikum:files:sidje_-_expokit_a_software_package_for_computing_matrix_exponentials.pdf| Sidje - Expokit: A Software Package for ComputingMatrix Exponentials}} Expokit is a Fortran/Matlab implementation of exponential integrators, the paper contains a lot of useful details on implementing exponential integrators. | ||