Analysis of discrete energy-decay preserving schemes for Maxwell's equations in Cole-Cole dispersive medium
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915669208989696 |
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| author | Zhang, Guoyu Dong, Ziming Yin, Baoli Liu, Yang Li, Hong |
| author_facet | Zhang, Guoyu Dong, Ziming Yin, Baoli Liu, Yang Li, Hong |
| contents | This work investigates the design and analysis of energy-decay preserving numerical schemes for Maxwell's equations in a Cole-Cole (C-C) dispersive medium. A continuous energy-decay law is first established for the C-C model through a modified energy functional. Subsequently, a novel \(θ\)-scheme is proposed for temporal discretization, which is rigorously proven to preserve a discrete energy dissipation property under the condition \(θ\in [\fracα{2}, \frac{1}{2}]\). The temporal convergence rate of the scheme is shown to be first-order for \(θ\neq 0.5\) and second-order for \(θ= 0.5\). Extensive numerical experiments validate the theoretical findings, including convergence tests and energy-decay comparisons. The proposed SFTR-\(θ\) scheme demonstrates superior performance in maintaining monotonic energy decay compared to an alternative 2nd-order fractional backward difference formula, particularly in long-time simulations, highlighting its robustness and physical fidelity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of discrete energy-decay preserving schemes for Maxwell's equations in Cole-Cole dispersive medium Zhang, Guoyu Dong, Ziming Yin, Baoli Liu, Yang Li, Hong Numerical Analysis This work investigates the design and analysis of energy-decay preserving numerical schemes for Maxwell's equations in a Cole-Cole (C-C) dispersive medium. A continuous energy-decay law is first established for the C-C model through a modified energy functional. Subsequently, a novel \(θ\)-scheme is proposed for temporal discretization, which is rigorously proven to preserve a discrete energy dissipation property under the condition \(θ\in [\fracα{2}, \frac{1}{2}]\). The temporal convergence rate of the scheme is shown to be first-order for \(θ\neq 0.5\) and second-order for \(θ= 0.5\). Extensive numerical experiments validate the theoretical findings, including convergence tests and energy-decay comparisons. The proposed SFTR-\(θ\) scheme demonstrates superior performance in maintaining monotonic energy decay compared to an alternative 2nd-order fractional backward difference formula, particularly in long-time simulations, highlighting its robustness and physical fidelity. |
| title | Analysis of discrete energy-decay preserving schemes for Maxwell's equations in Cole-Cole dispersive medium |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.10560 |