Related papers: Alternating direction implicit time integrations f…
Imposition methods of interface conditions for the second-order wave equation with non-conforming grids is considered. The spatial discretization is based on high order finite differences with summation-by-parts properties. Previously…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
This paper deals with the numerical solution of the Heston partial differential equation that plays an important role in financial option pricing, Heston (1993, Rev. Finan. Stud. 6). A feature of this time-dependent, two-dimensional…
Aiming at solving large-scale learning problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the learning problem as a consensus problem, the ADMM can…
A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close…
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…
In this paper, we focus on an asynchronous distributed optimization problem. In our problem, each node is endowed with a convex local cost function, and is able to communicate with its neighbors over a directed communication network.…
Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…
In order to run Computational Fluid Dynamics (CFD) codes on large scale infrastructures, parallel computing has to be used because of the computational intensive nature of the problems. In this paper we investigate the ADAPT platform where…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
The escalating adoption of diffusion models for applications such as image generation demands efficient parallel inference techniques to manage their substantial computational cost. However, existing diffusion parallelism inference schemes…
There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…
Since numerical computing with MATLAB offers a wide variety of advantages, such as easier developing and debugging of computational codes rather than lower-level languages, the popularity of this tool is significantly increased in the past…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute…
Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers in an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a…
We propose a novel finite-difference time-domain (FDTD) scheme for the solution of the Maxwell's equations in which linear dispersive effects are present. The method uses high-order accurate approximations in space and time for the…
An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid…
In this paper, by introducing two temporal-derivative-dependent auxiliary variables, a linearized and decoupled fourth-order compact finite difference method is developed and analyzed for the nonlinear coupled bacterial systems. The…
As a follow up to \cite{Causley2013}, we provide a detailed description of the numerical implementation of an O(N), A-stable, second order accurate solution of the wave equation, constructed from semi-discrete boundary value problems. We…