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• W2913346702 abstract "Revisionist integral deferred correction (RIDC) methods are time parallel predictor-correctormethods used to solve initial value problems (IVPs). The prediction andthe correction formulae are designed in such a way so that the prediction and thecorrection steps can be computed simultaneously. More than one computing core canbe used at a time to correct the approximate solutions at different correction levels.The multi-core implementation can improve the efficiency of the methods in terms ofruntime.In our thesis, we ultimately wish to solve parabolic partial differential equations(PDEs) numerically by combining the spatial adaptive moving mesh method with thetime parallel revisionist integral deferred correction (RIDC) method. To do so, weexpand an existing RIDC library to handle systems of IVPs of the form L(t, y)y′ =f(t, y), y ∈ Rn. Discretization of a physical PDE by the moving method of linescoupled with a semi-discretized moving mesh PDE results in a system of IVPs ofthe form L(t, y)y′ = f(t, y), where y(t) is a vector consisting of the physical solutionu ∈ Rn and the mesh x ∈ Rn, and L(t, y) is a state dependent square matrix. Weachieve a RIDC implementation for this family of IVPs by systematically expandingthe existing RIDC formulation and software. We have verified our derived formulaeand software with relevant examples." @default.
• W2913346702 created "2019-02-21" @default.
• W2913346702 creator A5008956473 @default.
• W2913346702 date "2018-09-01" @default.
• W2913346702 modified "2023-09-23" @default.
• W2913346702 title "Revisionist integral deferred correction methods with application to the moving method of lines" @default.
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• W2913346702 hasPublicationYear "2018" @default.
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