Related papers: Parallel-in-time high-order multiderivative IMEX s…

We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs…

Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…

We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…

In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the…

In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to…

In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…

Recently, a 4th-order asymptotic preserving multiderivative implicit-explicit (IMEX) scheme was developed (Sch\"utz and Seal 2020, arXiv:2001.08268). This scheme is based on a 4th-order Hermite interpolation in time, and uses an approach…

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a…

Revisionist integral deferred correction (RIDC) methods are a family of parallel--in--time methods to solve systems of initial values problems. The approach is able to bootstrap lower order time integrators to provide high order…

We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…

We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…

When applying the classical multistep schemes for solving differential equations, one often faces the dilemma that smaller time steps are needed with higher-order schemes, making it impractical to use high-order schemes for stiff problems.…

We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…

We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…

We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…

Numerical solutions to the Eikonal equation are computed using variants of the fast marching method, the fast sweeping method, and the fast iterative method. In this paper, we provide a unified view of these algorithms that highlights their…

First-order methods based on the PDHG algorithm have recently emerged as a viable option for efficiently solving large-scale linear programming problems. One highly desirable property of these methods is that they can make effective use of…

Following a series of high-profile drug safety disasters in recent years, many countries are redoubling their efforts to ensure the safety of licensed medical products. Large-scale observational databases such as claims databases or…