Related papers: A compiler for variational forms
Standardization of data formats in a scientific discipline brings a range of benefits to researchers, as it enables the sharing of workflows and solutions to common problems, provides the foundation for generically useful tools that can be…
This paper introduces the Fractal-Chaotic Oscillation Co-driven (FCOC) framework, a novel paradigm for financial volatility forecasting that systematically resolves the dual challenges of feature fidelity and model responsiveness. FCOC…
This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding,…
FormCalc is a Mathematica package for the automatic computation of tree-level and one-loop Feynman amplitudes. It accepts diagrams generated by FeynArts, simplifies them, and generates a complete Fortran code for their numerical evaluation.…
The numerical implementation of finite element discretization method for the stream function formulation of a linearized Navier-Stokes equations is considered. Algorithm 1 is applied using Argyris element. Three global orderings of nodes…
In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
The resolvent analysis of McKeon & Sharma (2010) recasts the Navier-Stokes equations into an input/output form in which the nonlinear term is treated as a forcing that acts upon the linear dynamics to yield a velocity response. The…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
In this paper we introduce a novel quantifier elimination method for conjunctions of linear real arithmetic constraints. Our algorithm is based on the Fourier-Motzkin variable elimination procedure, but by case splitting we are able to…
In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…
We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems, a grand challenge in computational science. State-of-the-art methods for these problems are severely limited…
This paper details the development and application of an $h$-adaptive finite element method for the numerical solution of the \textit{Falkner-Skan equation}. A posteriori error estimation governs the adaptivity of the mesh, specifically the…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
We provide a convergence analysis for a new fractional time-stepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent,…
Optimization of beamlines and lattices is a common problem in accelerator physics, which is usually solved with semi-analytical methods and numerical optimization routines. However, these are usually of the gradient-free or…