Numerical methods for ordinary differential equations: Difference between revisions

Revision as of 21:12, 15 November 2023

Revision as of 21:26, 15 November 2023

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Some IVPs require integration at such high temporal resolution and/or over such long time intervals that classical serial time-stepping methods become computationally infeasible to run in real-time (e.g. IVPs in numerical weather prediction, plasma modelling, and molecular dynamics). [[Parallel-in-time]] (PinT) methods have been developed in response to these issues in order to reduce simulation runtimes through the use of [[parallel computing]].

Early PinT methods (the earliest being proposed in the 1960s)<ref> {{cite journal |last=Nievergelt |first=Jürg |date=1964 |title=Parallel methods for integrating ordinary differential equations |journal=Communications of the ACM |volume=7 |issue=12 |pages=731–733 |doi=10.1145/355588.365137 |s2cid=6361754 |doi-access=free}}</ref>) were initially overlooked by researchers due to the fact that the parallel computing architectures that they required were not yet widely available. With more computing power available, interest was renewed in the early 2000s with the development of [[Parareal]], a flexible, easy-to-use PinT algorithm that is suitable for solving a wide variety of IVPs. The advent of [[exascale computing]] has meant that PinT algorithms are attracting increasing research attention and are being developed in such a way that they can harness the world's most powerful [[Supercomputer|supercomputers]]. The most popular methods as of 2023 include Parareal, PFASST, ParaDiag, and MGRIT.<ref>{{Cite web |title=Parallel-in-Time.org |url=https://parallel-in-time.org/methods/index.html |access-date=15 November 2023 |website=Parallel-in-Time.org}}</ref>.

Early PinT methods (the earliest being proposed in the 1960s<ref>

{{cite journal |last=Nievergelt |first=Jürg |date=1964 |title=Parallel methods for integrating ordinary differential equations |journal=Communications of the ACM |volume=7 |issue=12 |pages=731–733 |doi=10.1145/355588.365137 |s2cid=6361754 |doi-access=free}}</ref>) were initially overlooked by researchers due to the fact that the parallel computing architectures that they required were not yet widely available. With more computing power available, interest was renewed in the early 2000s with the development of [[Parareal]], a flexible, easy-to-use PinT algorithm that is suitable for solving a wide variety of IVPs. The advent of [[exascale computing]] has meant that PinT algorithms are attracting increasing research attention and are being developed in such a way that they can harness the world's most powerful [[Supercomputer|supercomputers]]. The most popular methods as of 2023 include Parareal, PFASST, ParaDiag, and MGRIT<ref>{{Cite web |title=Parallel-in-Time.org |url=https://parallel-in-time.org/methods/index.html |access-date=15 November 2023 |website=Parallel-in-Time.org}}</ref>.

== Analysis ==