Abstract
The method of regularized stokeslets is a powerful numerical approach to solve the Stokes flow equations for problems in biological fluid mechanics. A recent variation of this method incorporates a...
Highlights
The development of numerical methods for the solution of Stokes flow has had significant impact on the study of problems in biological fluid dynamics [1, 14, 15, 20, 21, 23] and vice versa
While there have been many powerful methods developed over the past few decades, one of the most effective and accessible tools for solving such problems is the method of regularized stokeslets, conceived of and developed by Cortez and colleagues [2, 7, 8, 9, 10, 11], and recently extended to incorporate the use of the fast multipole method [16]
Instead the objective is to strike a balance between accuracy, efficiency, and ease of use, the latter through avoiding the need to generate a smooth surface geometry ormesh."" The present method has a significantly reduced error compared to the classical (Nystr\o"m) discretization, while retaining a simplicity which enables its implementation by nonexperts for the investigation of many biologically relevant problems in Stokes flow
Summary
The development of numerical methods for the solution of Stokes flow has had significant impact on the study of problems in biological fluid dynamics [1, 14, 15, 20, 21, 23] and vice versa. Having developed the analysis to understand the quadrature error inherent in a single evaluation of the kernel, it is of practical use to assess how this error scales in a full application of the nearest-neighbor discretization (when solving a resistance problem, for example). Provided again that Q is not too large (which will cause CQ to correspondingly increase), is clear that this method resolves a problem that affects boundary element methods for Stokes flow by ensuring that the condition number remains bounded as the size of the force elements approaches zero The bounds that this analysis places on the condition number of the matrix A are practically very useful when solving problems with the nearest-neighbor discretization.
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