Related papers: A parallel iterative method for variational integr…
Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value…
We present new algorithms for the parallelization of Eulerian-Lagrangian interaction operations in the immersed boundary method. Our algorithms rely on two well-studied parallel primitives: key-value sort and segmented reduce. The use of…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
We present a massively parallel Lagrange decomposition method for solving 0--1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows to…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…
This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…
We present a parallel GPU-accelerated solver for branch Model Predictive Control problems. Based on iterative LQR methods, our solver exploits the tree-sparse structure and implements temporal parallelism using the parallel scan algorithm.…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are…
Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…