Related papers: Numerical efficiency of explicit time integrators …
Large language models (LLMs) power many state-of-the-art systems in natural language processing. However, these models are extremely computationally expensive, even at inference time, raising the natural question: when is the extra cost of…
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…
We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…
Accurate performance estimation of future many-node machines is challenging because it requires detailed simulation models of both node and network. However, simulating the full system in detail is unfeasible in terms of compute and memory…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
We present a progress report on the Cluster Processor, a special-purpose computer system for the Wolff simulation of the three-dimensional Ising model, including an analysis of simulation results obtained thus far. These results allow,…
This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…
Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and…
This article is concerned with a new filtered two-step variational integrator for solving the charged-particle dynamics in a mildly non-uniform moderate or strong magnetic field with a dimensionless parameter $\varepsilon$ inversely…
We show that adaptive time stepping in particle accelerator simulation is an enhancement for certain problems. The new algorithm has been implemented in the OPAL (Object Oriented Parallel Accelerator Library) framework, and is compared to…
Coherent multiport interferometers are a promising approach to realize matrix multiplication in integrated photonics. However, most known architectures - such as MZI and beamsplitter meshes, as well as more general interferometers - suffer…
Embedded Field-Programmable Gate Arrays (eFPGAs) allow for the design of hardware accelerators of edge Machine Learning (ML) applications at a lower power budget compared with traditional FPGA platforms. However, the limited eFPGA logic and…
The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
We construct a particle integrator for nonrelativistic particles by means of the splitting method based on the exact flow of the equation of motion of particles in the presence of constant electric and magnetic field. This integrator is…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
Features in the primordial power spectrum require numerical methods that are both accurate and scalable across the wide class of multifield inflationary models that produce them. Sharp turns in the background trajectories, induced by either…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
Simulation of geothermal systems is challenging due to coupled physical processes in highly heterogeneous media. Combining the exponential Rosenbrock--Euler and Rosenbrock-type methods with control-volume (two-point flux approximation)…
We compare the accuracy, convergence rate and computational cost of eigenerosion (EE) and phase-field (PF) methods. For purposes of comparison, we specifically consider the standard test case of a center-crack panel loaded in biaxial…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…