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Many problems in applied mathematics require the evaluation of the sum of N Gaussians at M points in space. The work required for direct evaluation grows like NM as N and M increase; this makes it very expensive to carry out such calculations on a large scale. In this paper, an algorithm is presented which evaluates the sum of N Gaussians at M arbitrarily(More)
BACKGROUND AND OBJECTIVES In autosomal dominant polycystic kidney disease (ADPKD), progressive kidney cyst formation commonly leads to ESRD. Because important manifestations of ADPKD may be evident in childhood, early intervention may have the largest effect on long-term outcome. Statins are known to slow progressive nephropathy in animal models of ADPKD.(More)
A new numerical method for solving geometric moving interface problems is presented. The method combines a level set approach and a semi-Lagrangian time stepping scheme which is explicit yet unconditionally stable. The combination decouples each mesh point from the others and the time step from the CFL stability condition, permitting the construction of(More)
Level set methods for moving interface problems require efficient techniques for transforming an interface to a globally defined function whose zero set is the interface , such as the signed distance to the interface. This paper presents efficient algorithms for this " redistancing " problem. The algorithms use quadtrees and trian-gulation to compute global(More)
Accurate numericalintegrationof singularfunctions usually requireseither adaptivity or product integration. Both interfere with fast summation techniques and thus hamper large-scale computations. This paper presents a method for computing highly accurate quadrature formulas for singular functions which combine well with fast summation methods. Given the(More)