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A NEW PARALLEL KERNEL-INDEPENDENT FAST MULTIPOLE METHOD
Fast multipole methods adaptive algorithms massively parallel computing boundary integral equations N-body problems viscous flows
2015/7/15
We present a new adaptive fast multipole algorithm and its parallel implementation. The algorithm is kernel-independent in the sense that the evaluation of pairwise interactions does not rely on any a...
A massively parallel adaptive fast-multipole method on heterogeneous architectures
massively parallel fast-multipole method heterogeneous architectures
2015/7/15
We present new scalable algorithms and an implementation of the kernel-independent fast multiple method (KIFMM), employing hybrid distributed memory message passing (via MPI) and shared memory/streami...
The phase flow method
The phase flow method Ordinary differential equations Phase maps Phase flow Interpolation High-frequency wave propagation Geometrical optics Hamiltonian dynamics Ray equations Wave arrival times Eulerian and Lagrangian formulations
2015/7/14
This paper introduces the phase flow method, a novel, accurate and fast approach for constructing phase maps for nonlinear autonomous ordinary differential equations. The method operates by initially ...
Fast geodesics computation with the phase flow method
Geodesics Weighted geodesics Geodesic flow The phase flow method Manifolds Tangent bundles Charts Surface parameterization Spline interpolation
2015/7/14
This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface.The idea is to apply the recently developed phase flow method [L. Ying, E.J. Cande `s,...
FAST METHOD FOR HIGH-FREQUENCY ACOUSTIC SCATTERING FROM RANDOM SCATTERERS
acoustic scattering random domains uncertainty quantification boundary integral equations fast algorithms quasi–Monte Carlo methods
2015/7/14
This paper is concerned with the uncertainty quantification of high-frequency acoustic scattering from objects with random shape in two-dimensional space. Several new methods are introduced to efficie...
A Massively Parallel Adaptive Fast Multipole Method on Heterogeneous Architectures
Massively Parallel Adaptive Fast Multipole Method Heterogeneous Architectures
2015/7/14
We describe a parallel fast multipole method (FMM) for highly nonuniform distributions of particles. We employ both distributed memory parallelism (via MPI) and shared memory parallelism (via OpenMP a...
A PARALLEL DIRECTIONAL FAST MULTIPOLE METHOD
parallel fast multipole methods N-body problems scattering problems Helmholtz equation oscillatory kernels directional multilevel
2015/7/14
This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This cla...
The Technion school lecture notes:the moving plane method,or doing PDEs in a cafe
Technion school lecture notes moving plane method doing PDEs a cafe
2015/7/14
We will have two main characters in these notes: the maximum principle and the sliding method. The latter has a twin, the moving plane method–they are often so indistinguishable that we will count the...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method
2015/7/8
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
The Phase Flow Method
The phase flow method ordinary differential equations phase maps phase flow interpolation high-frequency wave propagation geometrical optics Hamiltonian dynamics ray equations wave arrival times Eulerian and Lagrangian formulations
2015/6/17
This paper introduces the phase flow method, a novel, accurate and fast approach for constructing phase maps for nonlinear autonomous ordinary differential equations. The method operates by initially ...
Fast Geodesics Computation with the Phase Flow Method
Geodesics weighted geodesics geodesic flow the phase flow method manifolds tangent bundles charts surface parameterization spline interpolation
2015/6/17
This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface. The idea is to apply the recently developed phase flow method [15], an efficient and ...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method Theory Insights
2015/6/17
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Nesterov’s accelerated scheme convex optimization first-order methods differential equation restarting
2015/6/17
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can ...
A method for screening active effects in supersaturated designs
screening active supersaturated designs
2015/3/20
A method for screening active effects in supersaturated designs.
A Method for Generating Uniformly Scattered Points on the L p-norm Unit Sphere and Its Applications
Generating Uniformly Scattered Points L p-norm Unit Sphere and Its Applications
2015/3/20
A Method for Generating Uniformly Scattered Points on the L p-norm Unit Sphere and Its Applications.