Related papers: Case study of a differentiable heterogeneous multi…
The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using…
A unified numerically solvable framework for dispersion relations with arbitrary number of species drifting at arbitrary directions and with Krook collision is derived for linear uniform/homogenous kinetic plasma, which largely extended the…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference…
A non-linear system governed by multi-spatial and multi-temporal physics scales cannot be fully understood with a single diagnostic, as each provides only a partial view, leading to information loss. Combining multiple diagnostics may also…
In this study, we present a finite element solver for a thermodynamically consistent electrolyte model that accurately captures multicomponent ionic transport by incorporating key physical phenomena such as steric effects, solvation, and…
This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented…
High-order uncertain differential equation (HUDE) was introduced in literature. But the present method to solve a HUDE is incorrect. In this paper, we will rigorously prove some comparion theorems of high-order differential equations, and…
We present a cross-architecture high-order heterogeneous Navier-Stokes simulation solver, XFluids, for compressible reacting multicomponent flows on different platforms. The multi-component reacting flows are ubiquitous in many scientific…
Lattice Quantum Chromodynamics (Lattice QCD) is a quantum field theory on a finite discretized space-time box so as to numerically compute the dynamics of quarks and gluons to explore the nature of subatomic world. Solving the equation of…
Multiphysics incompressible fluid dynamics simulations play a crucial role in understanding intricate behaviors of many complex engineering systems that involve interactions between solids, fluids, and various phases like liquid and gas.…
We have developed an adaptive multigrid code for solving the Poisson equation in gravitational simulations. Finer rectangular subgrids are adaptively created in locations where the density exceeds a local level-dependent threshold. We…
Shock dynamics and nonlinear wave propagation are fundamental to computational fluid dynamics (CFD) and high-speed flow modeling. In this study, we developed explicit and implicit finite-difference solvers for the one-dimensional Burgers…
The excitation of a slow extraordinary wave in a overdense plasma from an ordinary wave impinging on the critical layer in the plane spanned by the density gradient and magnetic field is solved analytically by formulating the problem in…
We introduce an ODE solver for the PyTorch ecosystem that can solve multiple ODEs in parallel independently from each other while achieving significant performance gains. Our implementation tracks each ODE's progress separately and is…
Synchronized, independently tunable and focused $\mu$J-class laser pulses are used to release multiple electron populations via photo-ionization inside an electron-beam driven plasma wave. By varying the laser foci in the laboratory frame…
Coordinating growing grid flexibility under uncertainty is becoming increasingly important for efficient and reliable power-system operation. A core computational requirement is the efficient large-scale batched evaluation of AC power flow…
We develop a tool that enables domain experts to quickly generate numerical solvers for emerging multi-physics phenomena starting from a high-level description based on ordinary/partial differential equations and their initial and boundary…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
Time series alignment methods call for highly expressive, differentiable and invertible warping functions which preserve temporal topology, i.e diffeomorphisms. Diffeomorphic warping functions can be generated from the integration of…