A two-mechanism and multiscale compatible approach for solid state electrolytes of (Li-ion) batteries

All solid state batteries are claimed to be the next-generation battery system, in view of their safety accompanied by high energy densities. A new advanced, multiscale compatible, and fully three dimensional model for solid electrolytes is presented in this note. The response of the electrolyte is profoundly studied theoretically and numerically, analyzing the equilibrium and steady state behaviors, the limiting factors, as well as the most relevant constitutive parameters according to the sensitivity analysis of the model

An Adaptive Fuzzy based FEC Algorithm for Robust Video Transmission over Wireless Networks

Forward Error Correction (FEC) is a commonly adopted mechanism to mitigate packet loss/bit error during real-time communication. An adaptive, Fuzzy based FEC algorithm to provide a robust video quality metric for multimedia transmission over wireless networks has been proposed to optimize the redundancy of the generated code words from a Reed-Solomon encoder and to save the bandwidth of the network channel. The scheme is based on probability estimations derived from the data loss rates related to the recovery mechanism at the client end. By applying the adaptive FEC, the server uses the reports to predict the next network loss rate using a curve-fitting technique to generate the optimized number of redundant packets to meet specific residual error rates at the client end. Simulation results in the cellular system show that the video quality is massively adapted to the optimized FEC codes based on the probability of packet loss and packet correlation in a wireless environment

Domain decomposition method of stochastic PDEs: A two-level scalable preconditioner

For uncertainty quantification in many practical engineering problems, the stochastic finite element method (SFEM) may be computationally challenging. In SFEM, the size of the algebraic linear system grows rapidly with the spatial mesh resolution and the order of the stochastic dimension. In this paper, we describe a non-overlapping domain decomposition method, namely the iterative substructuring method to tackle the large-scale linear system arising in the SFEM. The SFEM is based on domain decomposition in the geometric space and a polynomial chaos expansion in the probabilistic space. In particular, a two-level scalable preconditioner is proposed for the iterative solver of the interface problem for the stochastic systems. The preconditioner is equipped with a coarse problem which globally connects the subdomains both in the geometric and probabilistic spaces via their corner nodes. This coarse problem propagates the information quickly across the subdomains leading to a scalable preconditioner. For numerical illustrations, a two-dimensional stochastic elliptic partial differential equation (SPDE) with spatially varying non-Gaussian random coefficients is considered. The numerical scalability of the the preconditioner is investigated with respect to the mesh size, subdomain size, fixed problem size per subdomain and order of polynomial chaos expansion. The numerical experiments are performed on a Linux cluster using MPI and PETSc parallel libraries

Scalable two-level domain decomposition algorithm for stochastic systems

For efficient numerical solution of stochastic partial differential equations (SPDEs) having random operators, a number of non-overlapping domain decomposition algorithms are formulated using the polynomial chaos expansion (PCE) (Sarkar, Benabbou, & Ghanem 2009, Subber & Sarkar 2010a, Subber & Sarkar 2010b, Subber & Sarkar 2011, Subber & Sarkar 2012b, Subber & Sarkar 2012a, Subber 2012, Subber & Sarkar 2013). The computational framework is based on the intrusive spectral stochastic finite element method (Ghanem & Spanos 1991, Ghanem & Spanos 1990, Ghanem, Saad, & Doostan 2007, Ghanem & Kruger 1996, Ghanem & Doostan 2006, Maitre & Knio 2010, Maitre, Knio, Debusschere, Najm, & Ghanem 2003, Eiermann & Ernst 2007). These domain decomposition solvers effectively exploit supercomputers in order to tackle the large-scale linear system when (1) the finite element mesh resolution is high and (2) the number of random systems parameters are large.The efficiency of some of these domain decomposition algorithms is primarily governed by the coarse grid used to construct a two-level parallel preconditioner for the preconditioned conjugate gradient method (PCGM) for the iterative solution of the linear system (e.g. Subber & Sarkar 2010a, Subber & Sarkar 2010b, Subber & Sarkar 2011, Subber & Sarkar 2012b, Subber & Sarkar 2012a, Subber 2012, Subber & Sarkar 2013). In this paper, we study the performance of a stochastic version of a primal two-level domain decomposition preconditioner (Subber & Sarkar 2010b, Subber & Sarkar 2011) through an application involving the stochastic seepage under a dam, implemented using MPI (MPI 2009) and PETSc (Balay, Buschelman, Gropp, Kaushik, Knepley, McInnes, Smith, & Zhang 2009) parallel libraries and METIS (Karypis & Kumar 1995) graph partitioning software

Domain decomposition of stochastic PDEs: A novel preconditioner and its parallel performance

A parallel iterative algorithm is described for efficient solution of the Schur complement (interface) problem arising in the domain decomposition of stochastic partial differential equations (SPDEs) recently introduced in [1,2]. The iterative solver avoids the explicit construction of both local and global Schur complement matrices. An analog of Neumann-Neumann domain decomposition preconditioner is introduced for SPDEs. For efficient memory usage and minimum floating point operation, the numerical implementation of the algorithm exploits the multilevel sparsity structure of the coefficient matrix of the stochastic system. The algorithm is implemented using PETSc parallel libraries. Parallel graph partitioning tool ParMETIS is used for optimal decomposition of the finite element mesh for load balancing and minimum interprocessor communication. For numerical demonstration, a two dimensional elliptic SPDE with non-Gaussian random coefficients is tackled. The strong and weak scalability of the algorithm is investigated using Linux cluster

Primal and dual-primal iterative substructuring methods of stochastic PDEs

A novel non-overlapping domain decomposition method is proposed to solve the large-scale linear system arising from the finite element discretization of stochastic partial differential equations (SPDEs). The methodology is based on a Schur complement based geometric decomposition and an orthogonal decomposition and projection of the stochastic processes using Polynomial Chaos expansion. The algorithm offers a direct approach to formulate a two-level scalable preconditioner. The proposed preconditioner strictly enforces the continuity condition on the corner nodes of the interface boundary, while weakly satisfying the continuity condition over the remaining interface nodes. This approach relates to a primal version of an iterative substructuring method. Next, a Lagrange multiplier based dual-primal domain decomposition method is introduced in the context of SPDEs. In the dual-primal method the continuity condition on the corner nodes is strictly satisfied while Lagrange multipliers are used to enforce continuity on the remaining part of the interface boundary. For numerical illustrations, a two dimensional elliptic SPDE with non-Gaussian random coefficients is considered. The numerical results demonstrate the scalability of these algorithms with respect to the mesh size, subdomain size, fixed problem size per subdomain, order of Polynomial Chaos expansion and level of uncertainty in the input parameters. The numerical experiments are performed on a Linux cluster using MPI and PETSc libraries

A domain decomposition method of stochastic PDEs: An iterative solution techniques using a two-level scalable preconditioner

Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic finite element method (SSFEM). In particular, a two-level scalable preconditioner is introduced in order to iteratively solve the large-scale linear system in the intrusive SSFEM using an iterative substructuring based domain decomposition solver. The implementation of the algorithm involves solving a local problem on each subdomain that constructs the local part of the preconditioner and a coarse problem that propagates information globally among the subdomains. The numerical and parallel scalabilities of the two-level preconditioner are contrasted with the previously developed one-level preconditioner for two-dimensional flow through porous media and elasticity problems with spatially varying non-Gaussian material properties. A distributed implementation of the parallel algorithm is carried out using MPI and PETSc parallel libraries. The scalabilities of the algorithm are investigated in a Linux cluster

A parallel time integrator for noisy nonlinear oscillatory systems

In this paper, we adapt a parallel time integration scheme to track the trajectories of noisy non-linear dynamical systems. Specifically, we formulate a parallel algorithm to generate the sample path of nonlinear oscillator defined by stochastic differential equations (SDEs) using the so-called parareal method for ordinary differential equations (ODEs). The presence of Wiener process in SDEs causes difficulties in the direct application of any numerical integration techniques of ODEs including the parareal algorithm. The parallel implementation of the algorithm involves two SDEs solvers, namely a fine-level scheme to integrate the system in parallel and a coarse-level scheme to generate and correct the required initial conditions to start the fine-level integrators. For the numerical illustration, a randomly excited Duffing oscillator is investigated in order to study the performance of the stochastic parallel algorithm with respect to a range of system parameters. The distributed implementation of the algorithm exploits Massage Passing Interface (MPI)