Related papers: Multigrid accelerated simulations for Twisted Mass…
We perform hybrid Monte-Carlo simulation of $N_f=2+1+1 $ lattice QCD with domain-wall quarks at the physical point. The simulation is carried out on the $ L^3 \times T = 64^3 \times 64 $ lattice with lattice spacing $a \sim 0.064 $ fm ($ L…
Ultrafast real-time dynamics are critical for understanding a broad range of physical processes. Real-time time-dependent density functional theory (rt-TDDFT) has emerged as a powerful computational tool for simulating these dynamics,…
We develop a matrix-free Full Approximation Storage (FAS) multigrid solver based on staggered finite differences and implemented on GPU in MATLAB. To enhance performance, intermediate variables are reused, and an X-shape Multi-Color…
Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential…
In order to develop fast inversion algorithms we have used overlap solvers in two dimensions. Lattice QED theory with U(1) group symmetry in two dimensional space-times dimensions has always been a testing ground for algorithms. By the…
The twisted reduced model of large $N$ QCD with two adjoint Wilson fermions is studied numerically using the Hybrid Monte Carlo method. This is the one-site model, whose large $N$ limit (large volume limit) is expected to be conformal or…
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…
Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently…
For an asymptotically free theory, a promising strategy for eliminating Critical Slowing Down (CSD) is na\"ive Fourier acceleration. This requires the introduction of gauge-fixing into the action, in order to isolate the asymptotically…
Quantum nanosystems involve the coupled dynamics of fermions or bosons across multiple scales in space and time. Examples include quantum dots, superconducting or magnetic nanoparticles, molecular wires, and graphene nanoribbons. The number…
Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to…
Multimodal image alignment involves finding spatial correspondences between volumes varying in appearance and structure. Automated alignment methods are often based on local optimization that can be highly sensitive to their initialization.…
Computer aided engineering of multi-time-scale plasma systems which exhibit a quasi-steady state solution are challenging due to the large number of time steps required to reach convergence. Machine learning techniques combined with…
We study how to simulate, efficiently, pulse field gradients (PFG) used in nuclear magnetic resonance (NMR). An efficient simulation requires discretization in time and space. We study both discretizations and provide a guideline to choose…
Three possibilities to speed up the Hybrid Monte Carlo algorithm are investigated. Changing the step-size adaptively brings no practical gain. On the other hand, substantial improvements result from using an approximate Hamiltonian or a…
The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard $\mathcal{O}(h^{-2})$ conditioning of second-order operators,…
A scheme for separating the high- and low-frequency molecular dynamics modes in Hybrid Monte Carlo (HMC) simulations of gauge theories with dynamical fermions is presented. The algorithm is tested in the Schwinger model with Wilson…
A general real-space multigrid algorithm for the self-consistent solution of the Kohn-Sham equations appearing in the state-of-the-art electronic-structure calculations is described. The most important part of the method is the multigrid…
The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid…