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There is no magical pill. If the study is modifying the mesh, you may need to limit the range of the study and/or attempt to understand how the mesh is changing during the study and create an initial mesh that is able to more robustly change during the study. A simple example would be if a 2D mesh contained square elements (ideal shape) but those elements are distorted (e.g., crushed) into thin rectangles during the study, you may want to begin with an initial mesh that contained rectangluar elements that distorted into a more square like shape. The bottomline is that you need to understand how the mesh is becoming distorted and attempt to create a mesh that is able to substain that amount of distortion.