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In this paper, we give the state of the art for the so called "mixed spectral elements" for Maxwell's equations. Several families of elements, such as edge elements and discontinuous Galerkin methods (DGM) are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is a novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements. [ABSTRACT FROM AUTHOR]

The alternately directional implicit (ADI) scheme is usually used in 3D depth migration. It splits the 3D square-root operator along crossline and inline directions alternately. In this paper, based on the ideal of data line, the four-way splitting schemes and their splitting errors for the finite-difference (FD) method and the hybrid method are investigated. The wavefield extrapolation of four-way splitting scheme is accomplished on a data line and is stable unconditionally. Numerical analysis of splitting errors show that the two-way FD migration have visible numerical anisotropic errors, and that four-way FD migration has much less splitting errors than two-way FD migration has. For the hybrid method, the differences of numerical anisotropic errors between two-way scheme and four-way scheme are small in the case of lower lateral velocity variations. The schemes presented in this paper can be used in 3D post stack or prestack depth migration. Two numerical calculations of 3D depth migration axe completed. One is the four-way FD and hybrid 3D post-stack depth migration for an impulse response, which shows that the anisotropic errors can be eliminated effectively in the cases of constant and variable velocity variations. The other is the 3D shot-profile prestack depth migration for SEG/EAEG benchmark model with two-way hybrid splitting scheme, which presents good imaging results. The Message Passing Interface (MPI) programme based on shot number is adopted. [ABSTRACT FROM AUTHOR]

This paper is concerned with the ill-posed problems of identifying a parameter in an elliptic equation which appears in may applications in science and industry. Its solution is obtained by applying trust region method to a nonlinear least squares error problem. Trust region method has long been a popular method for well-posed problems. This paper indicates that it is also suitable for all-posed problems. Numerical experiment is given to compare the trust region method with the Tikhonov regularization method. It seems that the trust region method is more promising. [ABSTRACT FROM AUTHOR]

In this paper, we consider the static output feedback (SOF) H∞-synthesis problem posed as a nonlinear semi-definite programming (NSDP) problem. Two numerical algorithms are developed to tackle the NSDP problem by solving the corresponding Karush-Kuhn-Tucker first-order necessary optimality conditions iteratively. Numerical results for various benchmark problems illustrating the performance of the proposed methods are given. [ABSTRACT FROM AUTHOR]

Consider the diffraction of a time-harmonic wave incident upon a periodic chiral structure. The diffraction problem may be simplified to a two-dimensional one. In this paper, the diffraction problem is solved by a finite element method with perfectly matched absorbing layers (PMLs). We use the PML technique to truncate the unbounded domain to a bounded one which attenuates the outgoing waves in the PML region. Our computational experiments indicate that the proposed method is efficient, which is capable of dealing with complicated chiral grating structures. Mathematics subject classification: 35Q60, 65L60, 78A45. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results. [ABSTRACT FROM AUTHOR]

In this paper, a nonmonotone method based on McCormick's second-order Armijo's step-size rule [7] for unconstrained optimization problems is proposed. Every limit point of the sequence generated by using this procedure is proved to be a stationary point with the second-order optimality conditions. Numerical tests on a set of standard test problems are presented and show that the new algorithm is efficient and robust. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to show that the quadrilateral mesh condition RDP(N, ψ) is only sufficient but not necessary for the optimal order error estimate of the Q1 isoparametric element in the H¹ norm. [ABSTRACT FROM AUTHOR]

In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method. We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method. [ABSTRACT FROM AUTHOR]

This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by tile implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton Krylov (JFNK) method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient, matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration methods are presented in confirmation of the theory and comparison of the performance of these methods. [ABSTRACT FROM AUTHOR]

In this paper, we study numerical approximations of a recently proposed phase field model for the vesicle membrane deformation governed by the variation of the elastic bending energy. To overcome the challenges of high order nonlinear differential systems and nonlinear constraints associated with the problem, we present the phase field bending elasticity model in a nested saddle point formulation. A mixed finite element method is then employed to compute the equilibrium configuration of a vesicle membrane with prescribed volume and surface area. Coupling the approximation results for a related linearized problem and the general theory of Brezzi-Rappaz-Raviart, optimal order error estimates for the finite element approximations of the phase field model are obtained. Numerical results are provided to substantiate the derived estimates. [ABSTRACT FROM AUTHOR]

In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements (if d - 2) or Brezzi-Douglas-Durfin-Fortin elements (if d = 3) on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented. [ABSTRACT FROM AUTHOR]

In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution [ABSTRACT FROM AUTHOR]

This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies. [ABSTRACT FROM AUTHOR]

This paper provides a simplified derivation for error estimates of the TRUNC plate element. The error analysis for the problem with mixed boundary conditions is also discussed. [ABSTRACT FROM AUTHOR]

Using least parameters, we expand the step-transition operator of any linear multi-step method (LMSM) up to O(τs+5) with order s = 1 and rewrite the expansion of the step-transition operator for s = 2 (obtained by the second author in a former paper). We prove that in the conjugate relation G3λτ oG1τ = G2τ o G3λτ with G1 being an LMSM, (1) the order of G2 can not be higher than that of G1; (2) if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new branch and bound algorithm for the solution of large scale separable concave programming problems. The largest distance bisection (LDB) technique is proposed to divide rectangle into sub-rectangles when one problem is branched into two subproblems. It is proved that the LDB method is a normal rectangle subdivision( NRS). Numerical tests on problems with dimensions from 100 to 10000 show that the proposed branch and bound algorithm is efficient for solving large scale separable concave programming problems, and convergence rate is faster than ωj-subdivision method. [ABSTRACT FROM AUTHOR]

In this paper, we present a new line search and trust region algorithm for unconstrained optimization problem with the trust region radius converging to zero. The new trust region algorithm performs a backtracking line search from the failed, point instead of resolving the subproblem when the trial step results in an increase in the objective function. We show that the algorithm preserves the convergence properties of the traditional trust region algorithms. Numerical results are also given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite element A -- ø method to approximate the eddy current equations with discontinuous coefficients in general three-dimensional Lipschitz polyhedral eddy current region. Nonmatching finite element meshes on the interface are considered and optimal error estimates are obtained. [ABSTRACT FROM AUTHOR]

The well known Wilson's brick is only convergent for regular cuboid meshes. In this paper a quasi-Wilson element of three dimension is presented which is convergent for any hexahedron meshes. Meanwhile the element is anisotropic, that is it can be used to any flat hexahedron meshes for which the regular condition is unnecessary. [ABSTRACT FROM AUTHOR]

Recently, two-phase schemes for removing salt-and-pepper and random-valued impulse noise are proposed in [6, 7]. The first phase uses decision-based median filters to locate those pixels which are likely to be corrupted by noise (noise candidates). In the second phase, these noise candidates are restored using a detail-preserving regularization method which allows edges and noise-free pixels to be preserved. As shown in [18], this phase is equivalent to solving a one-dimensional nonlinear equation for each noise candidate. One can solve these equations by using Newton's method. However, because of the edge preserving term, the domain of convergence of Newton's method will be very narrow. In this paper, we determine the initial guesses for these equations such that Newton's method will always converge. [ABSTRACT FROM AUTHOR]

This paper presents the dual bases for a new family of generalized Ball curves with a position parameter K, which includes the Bézier curve, generalized Said-Ball curve and some intermediate curves. Using the dual bases, the relative Marsden identity, conversion formulas of bases and control points of various curves are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the optimality conditions of a class of special nonsmooth programming min F(χ)-...|max{f[subi](χ),c[subi]}| which arises from L[sub1]-norm optimization, where c[subi] ∈ R is constant and f[subi] ∈ C¹, i = 1,2,...,m. These conditions can easily be tested by computer. [ABSTRACT FROM AUTHOR]

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h¾) and O(h ...) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for κ = 0 and κ = 1 respectively. [ABSTRACT FROM AUTHOR]

In this paper, the following two problems are considered: Problem I. Given S ∈ R[supn x p], X, B &isin R[supn x m], find A ∈ SR[subs, n] such that AX = B, where SR[subs, n] = {A ∈ R[supn x n]|χ[supT] (A - A[supT]) = 0, for all χ ∈ R(S)}. Problem II. Given A[sup*] ∈ R[supn x n], find  ∈ S[subE] such that ... where S[subE] is the solution set of Problem 1. The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem 1 are given. For problem II, the expression for the solution, a numerical algorithm and a numerical example are provided. [ABSTRACT FROM AUTHOR]

In this paper, a mortar finite element method for parabolic problem is presented. Multigrid method is used for solving the resulting discrete system. It is shown that the multigrid method is optional, i.e., the convergence rate is independent of the mesh size L and the time step parameter Τ. [ABSTRACT FROM AUTHOR]

This is the second part of the paper for the mathematical study of nonconforming rotated Q[sub 1] element (NRQ[sub 1] hereafter) on arbitrary quadrilateral meshes. Some Poincarè Inequalities are proved without assuming the quasi-uniformity of the mesh subdivision. A discrete trace inequality is also proved. [ABSTRACT FROM AUTHOR]

In this paper we present a trust region method of conic model for linearly constrained optimization problems. We discuss trust region approaches with conic model subproblems. Some equivalent variation properties and optimality conditions are given. A trust region algorithm based on conic model is constructed. Global convergence of the method is established. [ABSTRACT FROM AUTHOR]

Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is presented in this paper. When the objective function is bounded below and continuously differentiable, and the norm of the Hesse approximations increases at most linearly with the iteration number, we prove the global convergence of the algorithms. Limited numerical results are reported, which indicate that our new TR algorithm is competitive. [ABSTRACT FROM AUTHOR]

This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

The main purpose of this paper if to derive an explicit expression for Fourier-Chebyshev coefficient [multiple line equation(s) cannot be represented in ASCII text], which is initiatied by L. Gori and C.A. Micchelli. [ABSTRACT FROM AUTHOR]

In this paper the uniform convergence of Hermite-Fejér interpolation and Grünwald-type theorem of higher order on an arbitrary system of nodes are presented. [ABSTRACT FROM AUTHOR]