Related papers: Diagonalization-Based Parallel-in-Time Preconditio…
In this work, we propose a novel diagonalization-based preconditioner for the all-at-once linear system arising from the optimal control problem of parabolic equations. The proposed preconditioner is constructed based on an…
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…
This paper is concerned with a blood flow problem coupled with a slow plaque growth at the artery wall. In the model, the micro (fast) system is the Navier-Stokes equation with a periodically applied force and the macro (slow) system is a…
Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-boundary value method has been proposed and analyzed as an…
A parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method is described. It is based on formulation of BDDC with global matrices without explicit coarse problem. The implementation is based on the MUMPS…
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations.…
In this paper the Micro-Macro Parareal algorithm was adapted to PDEs. The parallel-in-time approach requires two meshes of different spatial resolution in order to compute approximations in an iterative way to a predefined reference…
Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…
The ParaDiag family of algorithms solves differential equations by using preconditioners that can be inverted in parallel through diagonalization. In the context of optimal control of linear parabolic PDEs, the state-of-the-art ParaDiag…
Topology optimization problems generally support multiple local minima, and real-world applications are typically three-dimensional. In previous work [I. P. A. Papadopoulos, P. E. Farrell, and T. M. Surowiec, Computing multiple solutions of…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
We develop a linearly-scaling variant of the Force Coupling Method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly-periodic geometry with either a…
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…
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…
We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address…