New techniques allow for more efficient boundary integral algorithms to compute the Dirichlet–Neumann map for Laplace’s equation in two-dimensional exterior domains. Novelties include a new post-processor which reduces the need for discretization points with 50 per cent, a new integral equation which reduces the error for resolved geometries with a factor equal to the system size, systematic us...

We prove the existence of piecewise polynomials strictly convex smooth functions which converge uniformly on compact subsets to the Aleksandrov solution of the Monge-Ampère equation. We extend the Aleksandrov theory to right hand side only locally integrable and on convex bounded domains not necessarily strictly convex. The result suggests that for the numerical resolution of the equation, it i...

nowadays, atomic force microscope is considered as a useful tool in the determination of intermolecular forces and surface topography with the resolution of nanometers. in this kind of microscope, micro cantilever is considered as the heart of the microscope and is used as a measuring tool.  this paper is aimed towards investigating the behavior of a piezoelectric micro cantilever with a triang...

We present an adaptive animation method for electrical discharges. Electric discharges can be simulated using the dielectric breakdown model. Regular discretization of the governing Laplace equation leads to huge equation systems, and the computational cost of solving the equations quickly becomes prohibitive at high resolutions, especially for simulations in 3D. In contrast, our method discret...

In this paper, the He’s parameter-expanding method (HPEM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES) are used in order to obtain analytical solutions to the non-linear modified Van der Pol’s oscillating circuit equation. The resolution protocols are applied to the ordinary Van der Pol equation, which annexed to conjoint delayed feedback and delay-related damping terms. The results ...

Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the super-replication price is the viscosity solution of a fully non-linear parabolic equation. As a by-product, we show how ε-optimal strategies can be constructed. Fina...

The Wigner equation provides an interesting mathematical limit, which recovers the constant field, ballistic Boltzmann equation. The peculiarities of a recently proposed Monte Carlo approach for solving the transient Wigner problem, based on generation and annihilation of particles are summarized. The annihilation process can be implemented at consecutive time steps to improve the Monte Carlo r...

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson’s equation, or equivalently under charge conservation, the Ampère’s one, which self-consistently rules the electric field ev...

The full application of Bayesian inference to inverse problems requires exploration of a posterior distribution that typically does not possess a standard form. In this context, Markov chain Monte Carlo (MCMC) methods are often used. These methods require many evaluations of a computationally intensive forward model to produce the equivalent of one independent sample from the posterior. We cons...

[1] Landscapes share important similarities with turbulence: both systems exhibit scale invariance (self-similarity) over a wide range of scales, and their behavior can be described using comparable dynamic equations. In particular, modified versions of the KardarParisi-Zhang (KPZ) equation (a low-dimensional analog to the Navier-Stokes equations) have been shown to capture important features o...