Recent results in the approximation of free boundaries
Remarks on Parameter Identification. I.
Remarks on the economic criterion - the Internal rate of return
The internal rate of return (IRR) together with the present value (PV) is used as a popular measure for financial project. When used appropriately, it can be a valuable aid in project acceptance or selection. The purpose of this article is to survey the facts about this criterion published so far. More, we investigate the cases of multiple or nonexistent IRRs and try to choose the relevant one and explain its economic meaning.
Resolution of the Maxwell equations in a domain with reentrant corners
Resonance behaviour of the spherical pendulum damper
The pendulum damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated using two approximate differential systems. Uni-directional harmonic external excitation at the suspension point is considered. Semi-trivial solutions and their stability are analyzed. The thorough analysis of the non-linear system using less simplification than it is used in the paper [2] is performed. Both approaches are compared and conclusions are drawn.
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
Sequential regularization of ill-posed problems involving unbounded operators
Shape optimization and trial methods for free boundary problems
Shape-from-Shading, viscosity solutions and edges.
Sharp L...-Error Estimates for Semilinear Elliptic Problems with Free Boundaries.
Shear flow past a flat plate in hydromagnetics.
Simulation of continuously deforming parabolic problems by Galerkin finite-elements method.
Solving initial-boundary value problems for coupled systems of partial differential equations
Some cases of numerical solution of differential equations describing the vortex-flow through three-dimensional axially symmetric channels
Some relatively new techniques for nonlinear problems.
Space-time adaptive -FEM: Methodology overview
We present a new class of self-adaptive higher-order finite element methods (-FEM) which are free of analytical error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methods do not contain any tuning parameters and work reliably with both low- and high-order finite elements. The methodology was used to solve various types of problems including thermoelasticity,...
Sparse grids for the Schrödinger equation
We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization. Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived that, in the best case, result in complexities and error estimates which are independent of the number of particles. Furthermore...
Spectral Approximation of the Periodic-Nonperiodic Navier-Stokes Equations.
Spherical basis function approximation with particular trend functions
The paper is concerned with the measurement of scalar physical quantities at nodes on the -dimensional unit sphere surface in the -dimensional Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider . We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful...