A variational method for electromagnetic diffraction in biperiodic structures
A variational method for parameter identification
A verified method for solving piecewise smooth initial value problems
In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview...
A viscosity solution method for Shape-From-Shading without image boundary data
In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884],...
A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space
In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition on the inertial term. Finally, we provide...
A wavelet based space-time adaptive numerical method for partial differential equations
A wavelet Galerkin finite-element method for the biot wave equation in the fluid-saturated porous medium.
A wavelet Galerkin method applied to partial differential equations with variable coefficients.
A wavelet interpolation Galerkin method for the simulation of MEMS devices under the effect of squeeze film damping.
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains
A weak regular splitting for singular linear systems.
A weaker affine covariant Newton-Mysovskikh theorem for solving equations
The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples...
A weakly over-penalized symmetric interior penalty method.
A weakly over-penalized symmetric interior penalty method for the biharmonic problem.
A weighted empirical interpolation method: a priori convergence analysis and applications
We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667–672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis...
A weighted-GCV method for Lanczos-hybrid regularization.
A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.
A well-posed shooting method for transferable DAE's.
A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag.
A ()-Stable Linear Multistep Methods for Stiff IVPs in ODEs
In this paper, a class of A()-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number and stiffly stable for and . Some numerical results are reported to illustrate the method.