Related papers: New Numerical Methods for Iterative or Perturbativ…
In this paper we consider stabilised finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three…
In this paper, we introduce a novel high-order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving…
The elucidation of many physical problems in science and engineering is subject to the accurate numerical modelling of complex wave propagation phenomena. Over the last decades, high-order numerical approximation for partial differential…
Computing the unit group and solving the principal ideal problem for a number field are two of the main tasks in computational algebraic number theory. This paper proposes efficient quantum algorithms for these two problems when the number…
We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We…
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. It is a natural extension of the classic conforming finite element method for discontinuous…
In this work, approximate solutions to the nonlinear Klein-Gordon equation are constructed by means of the Galerkin method. Specifically, it is shown how the dynamics of a real scalar field in $1+1$ dimensions subjected to Dirichlet…
Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions…
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can…
A considerable amount of attention has been given to discontinuous Galerkin methods for hyperbolic problems in numerical relativity, showing potential advantages of the methods in dealing with hydrodynamical shocks and other…
Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last…
This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D lattice-structured and periodic systems. The set of localized…
Unlike the fundamental forces of the Standard Model the quantum effects of gravity are still experimentally inaccessible. Rather surprisingly quantum aspects of gravity, such as massive gravitons, can emerge in experiments with fractional…
We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem…
When solving the Poisson equation by the finite element method, we use one degree of freedom for interpolation by the given Laplacian - the right hand side function in the partial differential equation. The finite element solution is the…
The Poisson-Boltzmann model is an effective and popular approach for modeling solvated biomolecules in continuum solvent with dissolved electrolytes. In this paper, we report our recent work in developing a Galerkin boundary integral method…
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…
In this article a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary…