Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method

Zeifang, Jonas; Thenery Manikantan, Arjun; Schütz, Jochen

doi:10.1016/j.amc.2023.128198

Applied Mathematics and Computation

2023

DOI: 10.1016/j.amc.2023.128198

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Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method

Jonas Zeifang,

Arjun Thenery Manikantan,

Jochen Schütz

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Cited by 6 publications

References 36 publications

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Functional‐preserving predictor‐corrector multiderivative schemes

Ranocha,

Schütz,

Theodosiou

2023

Proc Appl Math and Mech

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In this work, we develop a class of high‐order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite‐Birkhoff‐Predictor‐Corrector (HBPC) methods and the technique of relaxation for numerical methods of ordinary differential equations (ODEs). We explain the algorithm in detail and show numerical results for two‐ and three‐derivative methods, comparing relaxed and unrelaxed methods. The numerical results demonstrate that, at the slight cost of the relaxation, an improved scheme is obtained.

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Functional‐preserving predictor‐corrector multiderivative schemes

Ranocha,

Schütz,

Theodosiou

2023

Proc Appl Math and Mech

Self Cite

View full text Add to dashboard Cite

show abstract

Jacobian-free implicit MDRK methods for stiff systems of ODEs

Chouchoulis,

Schütz

2024

Applied Numerical Mathematics

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Multi-step Hermite-Birkhoff predictor-corrector schemes

Thenery Manikantan,

Schütz

2024

Applied Numerical Mathematics

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Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method

Cited by 6 publications

References 36 publications

Functional‐preserving predictor‐corrector multiderivative schemes

Functional‐preserving predictor‐corrector multiderivative schemes

Jacobian-free implicit MDRK methods for stiff systems of ODEs

Multi-step Hermite-Birkhoff predictor-corrector schemes

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