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In this manuscript, we present the development of implicit and implicit-explicit ADER and DeC methodologies within the DeC framework using the two-operators formulation, with a focus on their stability analysis both as solvers for ordinary…
This paper presents an efficient high-order sharp-interface method for solving the three-dimensional (3D) Poisson equation with Dirichlet boundary conditions on a nonuniform Cartesian grid with irregular domain boundaries. The new approach…
In this work, a new compact sixth order accurate finite difference scheme for the two and three-dimensional Helmholtz equation is presented. The main significance of the proposed scheme is that its sixth order leading truncation error term…
We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation…
The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…
Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even…
We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes,our method is based on reconstructing a piecewise-polynomial…
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonlinear equation, we use an iteration method to reformulate the…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
In this paper, we present a fully local second-order upwind scheme, applicable on generic meshes. This is done by hybridisation, which is achieved by introducing unknowns on each edge of the mesh. By doing so, fluxes only depend on values…
In this paper, we present a robust distributed model predictive control (DMPC) scheme for dynamically decoupled nonlinear systems which are subject to state constraints, coupled state constraints and input constraints. In the proposed…
Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the…
We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…
Simulations of single- and multi-species compressible flows with shock waves and discontinuities are conducted using a weighted compact nonlinear scheme (WCNS) with a newly developed sixth order localized dissipative interpolation. In…
In scenarios where high penetration of renewable energy sources (RES) is connected to the grid over long distances, the output of RES exhibits significant fluctuations, making it difficult to accurately characterize. The intermittency and…
Nonsmooth composite optimization with orthogonality constraints has a wide range of applications in statistical learning and data science. However, this problem is challenging due to its nonsmooth objective and computationally expensive…
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
We develop a method to combine Markov chain Monte Carlo (MCMC) and variational inference (VI), leveraging the advantages of both inference approaches. Specifically, we improve the variational distribution by running a few MCMC steps. To…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…