Local time-stepping methods permit to overcome the severe stability constraint on explicit caused by local mesh refinement without sacrificing explicitness. Diaz and Grote [SIAM J. Sci. Comput. 31 (2009), pp. 1985â??2014] proposed a leapfrog based (LF-LTS) method for time integration of second-order wave equations. Recently, optimal convergence rates were proved conforming FEM discretization, a...

Three-dimensional shape measurement is used in various fields such as robotics and inspection of industry production. It is requested to measure shape with high speed and high accuracy. It is also requested to make the system compact and low-cost. It is, however, difficult to satisfy these requests simultaneously for 3D shape measurement. In order to measure shape in real-time, Kato et al. prop...

In this paper, we propose and analyze a linear time stepping finite element method for abstract second order linear evolution problems. For such methods, we derive optimal order a posteriori error estimates and sharp a posteriori nodal error estimates using the energy approach and the duality argument. Based on these estimates, we further design an adaptive time stepping strategy for the previo...

A game-theoretic approach to the design of robust integrated guidance-control system for a moving-mass actuated kinetic warhead is presented. Feedback linearized form of the kinetic warhead dynamics and a high-order target model are used in the formulation. Nonlinear feedback solution to the robust finite-horizon target interception problem is derived using the recently developed multi-stepping...

Time-stepping finite element method (FEM) has become a powerful tool in solving transient electromagnetic fields. The formulation can include complex issues such as time harmonics and space harmonics, nonlinear magnetic property of iron materials, external circuit and mechanical motion in the system equations. However, as the derivatives of physical quantities are usually unknown at the initial...

The practical aspect in the parareal algorithm that it consist of using two solvers over different time stepping, the coarse and fine solvers to produce a rapid convergent iterative method for multi processors computations. The coarse solver solve the equation sequentially on the coarse time step while the fine solver use the information from the coarse solution to solve, in parallel, over the ...

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties–in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. This paper describes th...

The motivation of this project is to develop an efficient parallelized simulation of dynamics of large multi-particle systems on a parallel CPU/GPU high performance computing architecture. The work includes three parts: parallelization of the fast multipole method (FMM), multi-scale time stepping integrators and mapping the computation of nearby particles forces to GPUs. Possible applications o...