The push towards larger and larger computational platforms has made it possible for climate simulations to resolve climate dynamics across multiple spatial and temporal scales. This direction in climate simulation has created a strong need to develop scalable time-stepping methods capable of accelerating throughput on high performance computing. This work details the recent advances in the impl...

Numerous works in Computational Mechanics are dedicated to the simulation of multi-body systems with contact and friction. The case of dense multi-contact assemblies is one of the more complex one: the problem have often a large number of unknowns and the non uniqueness of solutions is usual. Moreover this problem becomes harder when the Coulomb’s friction or more complex laws are introduced. I...

This paper presents novel and efficient strategies to spatially adapt the amount of computational effort applied based on the local dynamics of a free surface flow, for classic weakly compressible SPH (WCSPH). Using a convenient and readily parallelizable block-based approach, different regions of the fluid are assigned differing time steps and solved at different rates to minimize computationa...

Leapfrog integration has been the method of choice in N-body simulations owing to its low computational cost for a symplectic integrator with second order accuracy. We introduce a new leapfrog integrator that allows for variable timesteps for each particle in large N-body simulations. Tests with single particles in fixed potentials show that it behaves as a symplectic integrator. We then examin...

The space-time geometric structure of Maxwell’s equations is examined and a subset of them is found to define a pair of exact discrete time-stepping relations. The desirability of adopting an approach to the discretization of electromagnetic problems which exploits this fact is advocated, and the name topological time-stepping for numerical schemes complying with it is suggested. The analysis o...

This paper is concerned with the solvability of implicit time-stepping methods for simulating the dynamics of multi-body systems. The standard approach is to select a time-step based on desired level of accuracy and computational efficiency of integration. Implicit methods impose an additional but often overlooked requirement that the resulting nonlinear root-finding problem is solvable and has...

Generally, two approaches have been used to study the nonlinear wave-structure interaction in the context of offshore engineering in recent years. One is based on the Stokes perturbation procedure in the frequency domain and has been applied to weak-nonlinear problems. The other is based on a full nonlinear solution to the resulting wave field by a time-stepping procedure with boundary conditio...

Classical alternating direction (AD) and fractional step (FS) methods for parabolic equations, based on some standard implicit time stepping procedure such as Crank-Nicolson, can have errors associated with the AD or FS perturbations that are much larger than the errors associated with the underlying time stepping procedure. We show that minor modi cations in the AD and FS procedures can virtua...

s 1. Gad P, Woodbridge J, Lavrov I, Gerasimenko Y, Zhong V, Roy RR, Sarrafzadeh M, Edgerton VR. Development of an electronic spinal bridge between the forelimbs and hindlimbs to facilitate quadrupedal stepping after a complete spinal cord transection. Society for Neuroscience, 2010. 2. Lavrov I, Nandra M, Choe J, Gad P, Zhong H, Roy RR, Burdick JW, Tai Y.C, and Edgerton VR. Further Development ...