A micro/macro parallel-in-time (parareal) algorithm applied to a climate model with discontinuous non-monotone coefficients and oscillatory forcing

We present the application of a micro/macro parareal algorithm for a 1-D energy balance climate model with discontinuous and non-monotone coefficients and forcing terms. The micro/macro parareal method uses a coarse propagator, based on a (macroscopic) 0-D approximation of the underlying (microscopic) 1-D model. We compare the performance of the method using different versions of the macro model, as well as different numerical schemes for the micro propagator, namely an explicit Euler method with constant stepsize and an adaptive library routine. We study convergence of the method and the theoretical gain in computational time in a realization on parallel processors. We show that, in this example and for all settings, the micro/macro parareal method converges in fewer iterations than the number of used parareal subintervals, and that a theoretical gain in performance of up to 10 is possible

An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation

A discrete random walk method on grids was proposed and used to solve the linearized Poisson-Boltzmann equation (LPBE) \cite{Rammile}. Here, we present a new and efficient grid-free random walk method. Based on a modified `` Walk On Spheres" (WOS) algorithm \cite{Elepov-Mihailov1973} for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. The new simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed.Comment: 12 pages, 5 figure

Unpacking capabilities underlying design (thinking) process

Engineering graduates must know how to frame and solve non-routine problems. While design classes explicitly teach problem framing and solving, it is lacking throughout much of the rest of the engineering curriculum and is often relegated to capstone classes at the end of the students’ educational experience. This paper explores problem framing and solving through the lens of experiential learning theory. It captures core problem framing and solving approaches from critical, design and systems thinking and concludes with a table of learning outcomes that might be drawn upon in designing an engineering curriculum that more fully develops the problem framing and solving capabilities of its students