Considering the varying effects of meniscal injuries on knee joint kinematics, these data provide insight into the pathological function of the ACL-injured knee joint during walking.
In this paper, we propose a novel scheme to accelerate integral equation solvers when applied to multiscale problems. These class of problems exhibit multiple length/frequency scales and arise when analyzing scattering/radiation from realistic structures where dense discretization is necessary to accurately capture geometric features. Solutions to the discretized integral equations due to these structures is challenging, due to their high computational cost and ill-conditioning of the resulting matrix system. The focus of this paper is on ameliorating the computational cost. Our approach will rely on exploiting the recently developed accelerated Cartesian expansion (ACE) algorithm to arrive at a method that is stable and efficient at low frequencies. These will then be integrated with the well known fast multipole method, thus forming a scheme that is wideband. Rigorous convergence estimates of this method are derived, and convergence and efficiency of the overall fast method is demonstrated. These are then integrated into an existing integral equation solver, whose efficiency is demonstrated for some practical problems.
Index Terms-Accelerated Cartesian expansion (ACE), Cartesian expansions, fast multipole method (FMM), fast solvers, integral equation (IE), multipole methods, multiscale, scattering, wideband.
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