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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…
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…
Stencil computations consume a major part of runtime in many scientific simulation codes. As prototypes for this class of algorithms we consider the iterative Jacobi and Gauss-Seidel smoothers and aim at highly efficient parallel…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
This paper proposes an efficient parallelised computation of field/circuit coupled systems co-simulated with the Waveform Relaxation (WR) technique. The main idea of the introduced approach lies in application of the parallel-in-time method…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…
Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…
We introduce new methods of equivalence checking and simulation based on Computing Range Reduction (CRR). Given a combinational circuit $N$, the CRR problem is to compute the set of outputs that disappear from the range of $N$ if a set of…
The goal of ranking and selection (R&S) procedures is to identify the best stochastic system from among a finite set of competing alternatives. Such procedures require constructing estimates of each system's performance, which can be…
We introduce a new open-source software library Jet, which uses task-based parallelism to obtain speed-ups in classical tensor-network simulations of quantum circuits. These speed-ups result from i) the increased parallelism introduced by…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
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…
In the last few decades, several novel algorithms have been designed for finding critical points on PES and the minimum energy paths connecting them. This has led to considerably improve our understanding of reaction mechanisms and kinetics…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Parallel algorithms designed for simulation and performance evaluation of single-server tandem queueing systems with both infinite and finite buffers are presented. The algorithms exploit a simple computational procedure based on recursive…
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…
Partial Differential Equation (PDE)-constrained optimization problems often take the form of an optimization of an objective function given as a sum of loss terms. Each function or gradient evaluation requires one or more PDE solves, which…