Related papers: A first-order computational algorithm for reaction…
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We establish optimal order a priori error estimates for implicit-explicit BDF methods for abstract semilinear parabolic equations with time-dependent operators in a complex Banach space settings, under a sharp condition on the…
A new class of implicit-explicit (IMEX) methods combined with a p-adaptive mixed finite element formulation is proposed to simulate the diffusion of reacting species. Hierarchical polynomial functions are used to construct an…
Some properties of a Local discontinuous Galerkin (LDG) algorithm are demonstrated for the problem of evaluting a second derivative $g = f_{xx}$ for a given $f$. (This is a somewhat unusual problem, but it is useful for understanding the…
This work is on a fast and accurate reduced basis method for solving discretized fractional elliptic partial differential equations (PDEs) of the form $\mathcal{A}^su=f$ by rational approximation. A direct computation of the action of such…
Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
A primal-dual accelerated stochastic gradient descent with variance reduction algorithm (PDASGD) is proposed to solve linear-constrained optimization problems. PDASGD could be applied to solve the discrete optimal transport (OT) problem and…
A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
We consider primal-dual mixed finite element methods for the advection--diffusion equation. For the primal variable we use standard continuous finite element space and for the flux we use the Raviart-Thomas space. We prove optimal a priori…
The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian Dynamics (BD) or…
Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…
We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems. While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…