Related papers: GPU-accelerated solutions of the nonlinear Schr\"o…
The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…
We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs), extending previous work to incorporate (a) Robin boundary conditions - which include Neumann and…
We provide an algorithm for evolving general spin-$s$ Gross-Pitaevskii / non-linear Schr\"odinger systems carrying a variety of interactions, where the $2s+1$ components of the `spinor' field represent the different spin-multiplicity…
Restricted solid on solid surface growth models can be mapped onto binary lattice gases. We show that efficient simulation algorithms can be realized on GPUs either by CUDA or by OpenCL programming. We consider a deposition/evaporation…
The Gross-Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose-Einstein condensates (BEC). However, in many physical situations, such as higher densities, this approximation unlikely suffices hence…
GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…
We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction ($z$), to a 2D mean-field equation. We address this problem for the…
We present new solutions to the nonautonomous nonlinear Schroedinger equation that may be realized through convenient manipulation of Bose-Einstein condensates. The procedure is based on the modulation of breathers through an analytical…
Starting from the 3D Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave-equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The…
An efficient method of solving the time-dependent Schr\"odinger equation for pure states is described: At each timestep, a restricted subspace of the total Hilbert space is systematically and naturally constructed via the image of repeated…
Power system state estimation (SE) is foundational for grid monitoring, yet conventional centralized solvers face increasing computational pressure as the system scale and real-time requirements grow. This paper presents a GPU-native…
Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often…
This paper presents the benchmarking and scaling studies of a GPU accelerated three dimensional compressible magnetohydrodynamic code. The code is developed keeping an eye to explain the large and intermediate scale magnetic field…
We extend the tensor-product direct solver from the Laplacian to the Schr\"odinger operator $-\Delta + V$. When the potential $V_1$ is separable, the operator $-\Delta + V_1$ is inverted or exponentiated at cost $O(N^{1+1/d})$ in $d$…
We report a novel algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent…
Coupled nonlinear Schr\"odinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow water waves. Despite their extensive applications, analytical…
We develop a highly optimized code for simulating the Edwards-Anderson Heisenberg model on graphics processing units (GPUs). Using a number of computational tricks such as tiling, data compression and appropriate memory layouts, the…
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii equation with both spherical and axial symmetries. We consider time-evolution problems…
Computational fluid dynamics and fluid-structure interaction simulations involving moving and deforming bodies is extremely hard. In this work, we present a graphical processing unit (GPU) optimized implementation of the sharp-interface…
Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…