The basic aim is to extend some results and concepts of nonautonomous second order differential systems with convex potentials to the new context of multi-time Poisson-gradient PDE systems with convex potential. In this sense, we prove that minimizers of a suitable action functional are multiple periodical solutions of a Dirichlet problem associated to the Euler-Lagrange equations. Automaticall...

The convergence order of finite elements is related to the polynomial order of the basis functions used on each element, with higher order polynomials yielding better convergence orders. However, two issues can prevent this convergence order from being achieved: the lack of regularity of the PDE solution and the poor approximation of curved boundaries by polygonal meshes. We show studies for La...

The convergence order of finite elements is related to the polynomial order of the basis functions used on each element, with higher order polynomials yielding better convergence orders. However, two issues can prevent this convergence order from being achieved: the poor approximation of curved boundaries by polygonal meshes and lack of regularity of the PDE solution. We show studies for Lagran...

In this chapter, we collect actual CPU time measurements of a number of prototypical PDE simulators for solving the Poisson equation, the linear elasticity equation, the heat conduction equation, the equations of nonlinear water waves, the incompressible Navier-Stokes equations, and many more. We show how these measurements can be used to establish performance models of the form: t = C n, which...

The contract is described and market examples given. Essential theoretical developments are introduced and cited chronologically. The principles and techniques of hedging and unique pricing are illustrated for the two simplest nontrivial examples: the classical Black-Scholes/Merton/Margrabe exchange option model brought somewhat upto-date from its form three decades ago, and a lesser exponentia...

This talk consists of a proof of part of Stenger’s SINC-PACK computer package (an approx. 400-page tutorial + about 250 Matlab programs) that one can always achieve separation of variables when solving linear elliptic, parabolic, and hyperbolic PDE (partial differential equations) via use of Sinc methods. Some examples illustrating computer solutions via SINC-PACK will nevertheless be given in ...

1 About This Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Hybrid FEM-RBF scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.1 One Dimensional Case . . . . . . . . . ....

The speed of iterative solvers for discretizations of partial differential equations (PDEs) is a significant bottleneck in the performance of codes designed to solve large-scale electromagnetic inverse problems. A single data inversion requires solving Maxwell’s equations dozens if not hundreds of times. An inherent difficulty in geophysical contexts is that the conductivity and permeability co...

Using a new stability estimate for the difference of square roots two solutions Vlasov–Poisson equation, we obtain convergence in L 2 norm Wigner transform solution Hartree equation with Coulomb potential to rate proportional ℏ. This improves ℏ 3/4-ε obtained [L. Lafleche, C. Saffirio: Analysis & PDE, appear]. Another reason interest this paper is method, reminiscent ones used prove mean-field ...