We show that the discrete operator stemming from time-space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines projection techniques with the full exploitation of the entry-wise structure of the involved coefficient matrices is proposed. The resulting scheme is able to efficiently solve problems with a tremendous number of degrees of freedom while maintaining a low storage demand as illustrated in several numerical examples.
Matrix Equation Techniques for Certain Evolutionary Partial Differential Equations / Palitta D.. - In: JOURNAL OF SCIENTIFIC COMPUTING. - ISSN 0885-7474. - ELETTRONICO. - 87:3(2021), pp. 99.1-99.36. [10.1007/s10915-021-01515-x]
Matrix Equation Techniques for Certain Evolutionary Partial Differential Equations
Palitta D.
2021
Abstract
We show that the discrete operator stemming from time-space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines projection techniques with the full exploitation of the entry-wise structure of the involved coefficient matrices is proposed. The resulting scheme is able to efficiently solve problems with a tremendous number of degrees of freedom while maintaining a low storage demand as illustrated in several numerical examples.File | Dimensione | Formato | |
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