A shape-optimization technique for the capillary surface problem.
A shock-capturing discontinuous Galerkin method for the numerical solution of inviscid compressible flow
A shooting method for singular nonlinear second order Volterra integro-differential equations.
A short philosophical note on the origin of smoothed aggregations
We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively...
A sign preserving mixed finite element approximation for contact problems
This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite element method in which the unknowns are the displacement field and the contact pressure. The particularity of the method is that it furnishes a normal displacement field and a contact pressure satisfying the sign conditions of the continuous problem. The a priori error analysis of the method is closely linked with the study of a specific positivity...
A simple and efficient scheme for phase field crystal simulation
We propose an unconditionally stable semi-implicit time discretization of the phase field crystal evolution. It is based on splitting the underlying energy into convex and concave parts and then performing H-1 gradient descent steps implicitly for the former and explicitly for the latter. The splitting is effected in such a way that the resulting equations are linear in each time step and allow an extremely simple implementation and efficient solution. We provide the associated stability and error...
A simple counterexample to Kouchnirenko's conjecture.
A simple method for estimating the bounds of spectral radius of nonnegative irreducible matrices.
A simple proof of the spectral continuity of the Sturm-Liouville problem
The aim of this article is to present a simple proof of the theorem about perturbation of the Sturm-Liouville operator in Liouville normal form.
A Simple Rational Spline and its Application to Monotonic Interpolation to Monotonic Data.
A simple recursive estimator with on-line orthogonalization of the input sequence
A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets
A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewiseLipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output...
A Simplification of Stenger's Topological Degree Formula.
A Sinc Quadrature Rule for Hadamard Finite-part Integrals.
A single cell-based model of the ductal tumour microarchitecture.
A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation
A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is...
A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone
In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that...
A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations
The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.