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Analysis and Performance Evaluation of Adjoint-Guided Adaptive Mesh Refinement for Linear Hyperbolic PDEs Using Clawpack. (arXiv:1810.00927v1 [math.NA])
来源于:arXiv
Adaptive mesh refinement (AMR) is often used when solving time-dependent
partial differential equations using numerical methods. It enables time-varying
regions of much higher resolution, which can be used to track discontinuities
in the solution by selectively refining around those areas. The open source
Clawpack software implements block-structured AMR to refine around propagating
waves in the AMRClaw package. For problems where the solution must be computed
over a large domain but is only of interest in a small area this approach often
refines waves that will not impact the target area. We seek a method that
enables the identification and refinement of only the waves that will influence
the target area.
Here we show that solving the time-dependent adjoint equation and using a
suitable inner product allows for a more precise refinement of the relevant
waves. We present the adjoint methodology in general, and give details on how
this method has been implemented in AMRClaw. Examples fo 查看全文>>