The Positive-Definite Stability Analysis for Marching-on-in-Time Schemes

P.W.N. van Diepen; Martijn C. van Beurden; Roeland Dilz

doi:10.2528/PIERL23112406

The Positive-Definite Stability Analysis for Marching-on-in-Time Schemes

P.W.N. van Diepen (Corresponding author)
, Martijn C. van Beurden
, Roeland Dilz

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

24 Downloads (Pure)

Abstract

The positive-definite stability analysis (PDSA) is presented as a technique complementary to the companion-matrix stability analysis (CMSA). The PDSA is used to analyze the stability of marching-on-in-time (MOT) schemes. The heart of the PDSA is formed by the analysis on particular linear combinations of interaction matrices from an MOT scheme, which are assumed to be real-valued. If these are all positive definite, then the PDSA guarantees the stability of the scheme. The PDSA can be of a lower complexity than the full CMSA. The construction of the PDSA is shown and applied to two numerical examples.

Original language	English
Pages (from-to)	71-78
Number of pages	8
Journal	Progress In Electromagnetics Research (PIER) Letters
Volume	118
DOIs	https://doi.org/10.2528/PIERL23112406
Publication status	Published - 14 Mar 2024

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AB - The positive-definite stability analysis (PDSA) is presented as a technique complementary to the companion-matrix stability analysis (CMSA). The PDSA is used to analyze the stability of marching-on-in-time (MOT) schemes. The heart of the PDSA is formed by the analysis on particular linear combinations of interaction matrices from an MOT scheme, which are assumed to be real-valued. If these are all positive definite, then the PDSA guarantees the stability of the scheme. The PDSA can be of a lower complexity than the full CMSA. The construction of the PDSA is shown and applied to two numerical examples.

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JO - Progress In Electromagnetics Research (PIER) Letters

JF - Progress In Electromagnetics Research (PIER) Letters

ER -

The Positive-Definite Stability Analysis for Marching-on-in-Time Schemes

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