Related papers: Mixed-Precision in adaptive Runge-Kutta method for…
We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. The algorithms do not need to implement direct or adjoint sensitivity analysis…
Obtaining exact solutions to the Schr\"odinger equation in complex quantum systems poses significant challenges. In this context, numerical methods emerge as valuable tools for analyzing such systems. This article proposes a numerical…
In this work, we build upon the recently introduced Multiscale Robin Coupled Method with Oversampling and Smoothing (MRCM-OS) to develop two highly efficient iterative multiscale methods. The MRCM-OS methodology demonstrated the ability to…
To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floating-point formats beyond double precision (FP64). Double-word arithmetic…
Thanks to the computational power of modern cluster machines, numerical simulations can provide, with an unprecedented level of details, new insights into fluid mechanics. However, taking full advantage of this hardware remains challenging…
Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…
Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in…
We propose a mixed-configuration approximation based on single-band impurity solvers to efficiently study nonequilibrium multi-orbital systems at moderate computational cost. In this work, we merge the approach with the so-called auxiliary…
A fundamental problem in robotic perception is matching identical objects or data, with applications such as loop closure detection, place recognition, object tracking, and map fusion. While the problem becomes considerably more challenging…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
In this paper, the performance characteristics of different solution techniques and program packages to solve a large number of independent ordinary differential equation systems is examined. The employed hardware are an Intel Core i7-4820K…
We introduce a family of stochastic optimization methods based on the Runge-Kutta-Chebyshev (RKC) schemes. The RKC methods are explicit methods originally designed for solving stiff ordinary differential equations by ensuring that their…
This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…
This paper is concerned with the theory, construction and application of variable-stepsize implicit Peer two-step methods that are super-convergent for variable stepsizes, i.e., preserve their classical order achieved for uniform stepsizes…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
This paper investigates the energy conservation properties of explicit Runge--Kutta (RK) time discretizations for autonomous skew-symmetric systems. For linear problems, we present a general framework for constructing RK methods in which…
Mixed-precision arithmetic offers significant computational advantages for large-scale matrix computation tasks, yet preserving accuracy and stability in eigenvalue problems and the singular value decomposition (SVD) remains challenging.…
In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4…
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem…
In this paper we derive and analyze the properties of explicit singly diagonal implicit Runge-Kutta (ESDIRK) integration methods. We discuss the principles for construction of Runge-Kutta methods with embedded methods of different order for…