This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases a...

In this paper, classical and enriched finite element formulations to impose Bloch-periodic boundary conditions are proposed. Bloch-periodic boundary conditions arise in the description of wave-like phenomena in periodic media. We consider the quantum-mechanical problem in a crystalline solid, and derive the weak formulation and matrix equations for the Schrödinger and Poisson equations in a par...

Background: Lidocaine is a local anesthetic and antiarrhythmic agent. There are reports on accidental and intentional cases of poisoning following injection of lidocaine while rare are the fatal cases realized after oral ingestion of lidocaine. Suicidal poisoning with lidocaine pharmaceutical formulations is rare since no pharmaceutical dosage forms for oral use are available except gels and sp...

By using a suitable rescaled form of time-harmonic Maxwell’s equations, we numerically simulate the propagation of a slowly decaying electromagnetic wave, called surface plasmonpolariton, excited along a large conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. For this purpose, we derive a variational formulation that enables a direct numerical treatment of t...

water resources local governance can is one of the most influential collaborative approach in the water resources management. social monitoring of local stakeholders plays an important role in planning, resources management and water efficient governance. therefore to achieve this goal, social network analysis has been considered as an approach of analysis of the relationship among local stakeh...

In this paper we present an analysis of three di erent formulations of the discontinuous Galerkin method for di usion equations. The rst formulation yields an inconsistent and weakly unstable scheme, while the other two formulations, the local discontinuous Galerkin approach and the Baumann-Oden approach, give stable and convergent results. When written as nite di erence schemes, such a distinc...

This paper introduces a special setting of weakly supervised structured output learning, where the training data is a set of structured instances and supervision involves candidate labels for some local parts of the structure. We show that the learning problem with this weak supervision setting can be efficiently handled and then propose a large margin formulation. To solve the non-convex optim...

We propose an efficient iterative method to solve the mixed Stokes-Dracy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of equations. We apply a decoupled preconditioning technique requiring only good solvers for the local mixed-Darcy and Stokes subproblems. We prove that the method...

We introduce a mathematically rigorous formulation for nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization the weak form of problem. After proving well-posedness form, we demonstrate that solutions to converge corresponding local counterpart when data are appropriately prescribed. Several numerical tests in one two dimensions show applica...

As the plasmonic scatterers get much smaller than the wavelength of the incident light, local material models like the Drude model and the Lorentz model become inadequate to describe accurately the light-matter interactions. To overcome this, a sophisticated nonlocal hydrodynamic Drude model is investigated. In practice, it is further simplified and simulated with the curl-free approximation, w...