Related papers: A Parallel-In-Time Adjoint Sensitivity Analysis fo…
Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent PDEs in modern high-performance computing environments. While these…
This paper proposes a parallel in time (called also time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the same spirit as the domain decomposition that consists of breaking…
Stochastic reaction networks that exhibit bistability are common in many fields such as systems biology and materials science. Sampling of the stationary distribution is crucial for understanding and characterizing the long term dynamics of…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are…
Meta-optics promises compact, high-performance imaging and color routing. However, designing high-performance structures is a high-dimensional optimization problem: mapping a desired optical output back to a physical 3D structure requires…
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
The velocity field and the height at the surface of a dynamic ice sheet are observed. The ice sheets are modeled by the full Stokes equations and shallow shelf/shelfy stream approximations. Time dependence is introduced by a kinematic free…
This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations…
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties…
We develop a sensitivity function for the design of electron optics using an adjoint approach based on a form of reciprocity implicit in Hamilton's equations of motion. The sensitivity function, which is computed with a small number of…
A computational fluid dynamics code is differentiated using algorithmic differentiation (AD) in both tangent and adjoint modes. The two novelties of the present approach are 1) the adjoint code is obtained by letting the AD tool Tapenade…
Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a…
In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has…
Parallel-in-time methods have shown success for reducing the simulation time of many time-dependent problems. Here, we consider applying the multigrid-reduction-in-time (MGRIT) algorithm to a voltage-driven eddy current model problem.