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Adaptive mesh refinement (AMR) is often used when solving time-dependentpartial differential equations using numerical methods. It enables time-varyingregions of much higher resolution, which can be used to track discontinuitiesin the solution by selectively refining around those areas. The open sourceClawpack software implements block-structured AMR to refine around propagatingwaves in the AMRClaw package. For problems where the solution must be computedover a large domain but is only of interest in a small area this approach oftenrefines waves that will not impact the target area. We seek a method thatenables the identification and refinement of only the waves that will influencethe target area.  Here we show that solving the time-dependent adjoint equation and using asuitable inner product allows for a more precise refinement of the relevantwaves. We present the adjoint methodology in general, and give details on howthis method has been implemented in AMRClaw. Examples for linear acousticsequations are presented, and a computational performance analysis is conducted.The adjoint method is compared to AMR methods already available in the AMRClawsoftware, and the resulting advantages and disadvantages are discussed. Thecode for the examples presented is archived on Github.

Analysis and Performance Evaluation of Adjoint-Guided Adaptive Mesh Refinement for Linear Hyperbolic PDEs Using Clawpack