Related papers: A Parallel-in-Time Multigrid Preconditioner for Op…
This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…
We propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen--Cahn variational inequalities. The solver is seen to behave mesh independently and to have only a very mild…
We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
In this paper, we propose a generalized shift-splitting (GSS) preconditioner, along with its two relaxed variants to solve the double saddle point problem (DSPP). The convergence of the associated GSS iterative method is analyzed, and…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
This paper proposes a novel framework for addressing the challenge of autonomous overtaking and obstacle avoidance, which incorporates the overtaking path planning into Gaussian Process-based model predictive control (GPMPC). Compared with…
The Crank-Nicolson (CN) method is a well-known time integrator for evolutionary partial differential equations (PDEs) arising in many real-world applications. Since the solution at any time depends on the solution at previous time steps,…
This paper proposes a solution to the problem of smooth path planning for mobile robots in dynamic and unknown environments. A novel concept of Time-Warped Grid is introduced to predict the pose of obstacles in the environment and avoid…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
We present a stationary iteration based upon a block splitting for a class of indefinite least squares problem. Convergence of the proposed method is investigated and optimal value of the involving parameter is used. The induced…
We present a distributed parallel mesh curving method for virtual geometry. The main application is to generate large-scale curved meshes on complex geometry suitable for analysis with unstructured high-order methods. Accordingly, we devise…
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…
As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…
To ensure the system stability of the $\bf{\mathcal{H}_{2}}$-guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is formulated based on the sparsity of the gain matrix of the…
In this paper we propose to use model reduction techniques for speeding up the diagonalization-based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once systems from evolutionary PDEs. In particular, we use the…
Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are currently stagnate. This situation has created the well-known bottleneck for…
In recent years, solvers for finite-element discretizations of linear or linearized saddle-point problems, like the Stokes and Oseen equations, have become well established. There are two main classes of preconditioners for such systems:…
Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are…
Microgrids are increasingly being utilized to improve the resilience and operational flexibility of power grids, and act as a backup power source during grid outages. However, it necessitates that the microgrid itself could provide power to…