Related papers: New Numerical Methods for Iterative or Perturbativ…
Physics-informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and…
The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…
We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained…
In this paper, a new variational formulation based on discontinuous Galerkin technique for a reaction-diffusion problem is introduced, and the discontinuous Galerkin technique of this work is different from the general discontinuous…
A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
The set $\mathcal{Q}$ of quantum correlations is the collection of all possible probability distributions on measurement outcomes achievable by space-like separated parties sharing a quantum state. Since the original work of Tsirelson…
Large superconducting quantum circuits have a number of important applications in quantum computing. Accurately predicting the performance of these devices from first principles is challenging, as it requires solving the many-body…
We propose a new deterministic numerical scheme, based on the discontinuous Galerkin method, for solving the Boltzamnn equation for rarefied gases. The new scheme guarantees the conservation of the mass, momentum and energy. We avoid any…
Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques…
We investigate the application of efficient recursive numerical integration strategies to models in lattice gauge theory from quantum field theory. Given the coupling structure of the physics problems and the group structure within lattice…
Developments in algorithms over the past decade suggest that there is a new computational approach to a class of quantum field theories. This approach is based on rewriting the partition function in a representation similar to the…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
For the simulation of rectilinearly moving conductors across a magnetic field, the Galer-kin finite element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing Streamline…
In many cases of interest, the perturbative series based on conventional Feynman diagrams have a zero radius of convergence. Series with a finite radius of convergence can be obtained by either introducing a large field cutoff or by…
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual…