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111.
Runge–Kutta based convolution quadrature methods for abstract, well-posed, linear, and homogeneous Volterra equations, non
necessarily of sectorial type, are developed. A general representation of the numerical solution in terms of the continuous
one is given. The error and stability analysis is based on this representation, which, for the particular case of the backward
Euler method, also shows that the numerical solution inherits some interesting qualitative properties, such as positivity,
of the exact solution. Numerical illustrations are provided. 相似文献
112.
Joseph Majdalani Sjoerd W. Rienstra 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):289-308
The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators
and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe
the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum
and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid,
rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three
possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying
the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex.
This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression
that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general
and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method
of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions
that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach
to other complex fluid motions that are easier to capture using spherical coordinates. 相似文献
113.
A fictitious domain approach to the numerical solution of PDEs in stochastic domains 总被引:1,自引:0,他引:1
We present an efficient method for the numerical realization of elliptic PDEs in domains depending on random variables. Domains
are bounded, and have finite fluctuations. The key feature is the combination of a fictitious domain approach and a polynomial
chaos expansion. The PDE is solved in a larger, fixed domain (the fictitious domain), with the original boundary condition
enforced via a Lagrange multiplier acting on a random manifold inside the new domain. A (generalized) Wiener expansion is
invoked to convert such a stochastic problem into a deterministic one, depending on an extra set of real variables (the stochastic
variables). Discretization is accomplished by standard mixed finite elements in the physical variables and a Galerkin projection
method with numerical integration (which coincides with a collocation scheme) in the stochastic variables. A stability and
convergence analysis of the method, as well as numerical results, are provided. The convergence is “spectral” in the polynomial
chaos order, in any subdomain which does not contain the random boundaries. 相似文献
114.
This article introduces and analyzes a p-version FEM for variational inequalities resulting from obstacle problems for some quasi-linear elliptic partial differential
operators. We approximate the solution by controlling the obstacle condition in images of the Gauss–Lobatto points. We show
existence and uniqueness for the discrete solution u
p
from the p-version for the obstacle problem. We prove the convergence of u
p
towards the solution with respect to the energy norm, and assuming some additional regularity for the solution we derive
an a priori error estimate. In numerical experiments the p-version turns out to be superior to the h-version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation. 相似文献
115.
For a general K3 surface S of genus g, with 2 ≤ g ≤ 10, we prove that the intermediate Jacobians of the family of prime Fano threefolds of genus g containing S as a hyperplane section, form generically an algebraic completely integrable Hamiltonian system.
The first author is partially supported by grant MI1503/2005 of the Bulgarian Foundation for Scientific Research. 相似文献
116.
We study the connection between universal central extensions in the categories of precrossed and crossed modules. They are compared with several kinds of universal central extensions in the categories of groups, epimorphisms of groups, groups with operators and modules over a group. We study the relationship between the homologies defined in these categories. Applications to relative algebraic K-theory are also obtained. 相似文献
117.
In this paper we investigate the electrostatic problem of determining conductivity profiles from the knowledge of boundary
currents and voltages. We obtain an improved estimate for the voltage potential of a two-dimensional conductor having finitely
many circular inclusions and piecewise constant conductivity profile. We derive an asymptotic expansion for the voltage potential
in terms of the reference voltage potential and the location, size, and conductivity of the inhomogeneities. This representation
is used to formulate the nonlinear least squares problem for estimating the location and size of the inhomogeneities. Required
boundary data for the voltage potential are generated numerically by solving a system of integral equations. Computational
experiments are presented to demonstrate the effectiveness of our identification procedure. 相似文献
118.
Tokuzo Shiga 《Probability Theory and Related Fields》1997,108(3):417-439
Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf;
d
in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate
the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0.
Received: 21 May 1996 / In revised form: 2 February 1997 相似文献
119.
120.
Reinhard Farwig 《Acta Appl Math》1994,37(1-2):41-51
In this note, we discuss the reflection principle of the Stokes system in a half space for the threedimensional case, and of the biharmonic equation. Admitting different boundary conditions, we use the reflection principle to prove uniqueness of solutions of the Stokes system or the biharmonic equation in weightedLq-spaces 相似文献