We introduce and study parallel space-time domain decomposition methods for solving deterministic and stochastic parabolic equations. Traditional parallel algorithms solve parabolic problems time step by time step. The parallelism is restricted to each time step, and the algorithms are purely sequential in time. In this paper, we develop some overlapping Schwarz methods whose subdomains cover b...

We propose a robust data-driven model predictive control (MPC) scheme to linear time-invariant (LTI) systems. The uses an implicit description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only initially input-output trajectory as well upper bound the order of unknown system. First, we prove exponential s...

Overlapping Schwarz is a family of preconditioners for solving large sparse linear systems arising from the discretization of partial di erential equations see e g CS DW SBG Here we report on our preliminary experiences on using it in the implicit solution of unsteady Navier Stokes N S equations discretized on two dimensional unstructured meshes One of the advantages of implicit methods is that...

In this paper, a cell vertex finite volume algorithm is presented for the simulation of 3D incompressible fluid flow on unstructured meshes. The algorithm uses an efficient edge-based data structure. The artificial compressibility concept is employed to utilize the continuity equation to couple the pressure and velocity of the fluid. The steady solution is computed using an explicit multi-stage...

In this paper, numerical methods are developed and detailed in order to be able compute the ablation of metallic thermal protection system. complex multi-physics problem, state inside a solid domain two-phase viscous flow have computed. Since two fluid phases non-miscible, an extension five-equation model dissipative effects is considered. An operator splitting strategy used separate different ...

Given the substantial and growing scientific literature on implicit bias, the time has now come to confront a critical question: What, if anything, should we do about implicit bias in the courtroom? The author team comprises legal academics, scientists, researchers, and even a sitting federal judge who seek to answer this question in accordance with behavioral realism. The Article first provide...

In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales. We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale. This is due to the fact that such implicit methods cannot correctly capture non...

We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems. To solve reactiondiffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations. Along with the implementation of the method of lines, implicit or semi-implicit schemes are typical time...