Search results for "Computer Science::Numerical Analysis"
showing 10 items of 32 documents
"Table 2" of "Measurement of the Cross Section for Electromagnetic Dissociation with Neutron Emission in Pb-Pb Collisions at {\surd}sNN = 2.76 TeV"
2013
Mutual EMD -> at least one neutron is emitted by both Pb nuclei.
A Projected Algebraic Multigrid Method for Linear Complementarity Problems
2011
We present an algebraic version of an iterative multigrid method for obstacle problems, called projected algebraic multigrid (PAMG) here. We show that classical AMG algorithms can easily be extended to deal with this kind of problem. This paves the way for efficient multigrid solution of obstacle problems with partial differential equations arising, for example, in financial engineering.
Robust and Efficient IMEX Schemes for Option Pricing under Jump-Diffusion Models
2013
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump diffusion process. The schemes include the families of IMEX-midpoint, IMEXCNAB and IMEX-BDF2 schemes. Each family is defined by a convex parameter c ∈ [0, 1], which divides the zeroth-order term due to the jumps between the implicit and explicit part in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restrictions, the IMEX-midpoint fa…
A rigidity problem on the round sphere
2015
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere.
CVBEM solution for De Saint-Venant orthotropic beams under coupled bending and torsion
2014
The aim of this paper is to provide a solution for the coupled flexure–torsion De Saint Venant problem for orthotropic beams taking full advantage of the complex variable boundary element method (CVBEM) properly extended using a complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. The proposed method returns the complete stress field and the unitary twist rotation of the cross section at once by performing only line integrals. Numerical applications have been reported to show the validity and the efficiency of the proposed modified CVBEM to handle shear stress problems in the presence of ort…
Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
2011
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.
finite element methods
2017
Two robot patch recovery methods with built-in field equations and boundary conditions superconvergence similarities in standard and mixed finite element methods on the FEM for the Navier-Stokes equations in the domains with corner singularities projections in finite element analysis and application element analysis method and superconvergence quadratic interpolation polynomials in vertices of strongly regular triangulations explicit error bounds for a nonconforming finite element method analysis of the average efficiency of an error estimator on the mesh for difference schemes of higher accuracy for the heat-conduction equation shape design sensitivity formulae approximated by means of a r…
Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour
2019
Abstract The numerical solution of nonlinear convection-diffusion equations with nonlocal flux by explicit finite difference methods is costly due to the local spatial convolution within the convective numerical flux and the disadvantageous Courant-Friedrichs-Lewy (CFL) condition caused by the diffusion term. More efficient numerical methods are obtained by applying second-order implicit-explicit (IMEX) Runge-Kutta time discretizations to an available explicit scheme for such models in Carrillo et al. (2015) [13] . The resulting IMEX-RK methods require solving nonlinear algebraic systems in every time step. It is proven, for a general number of space dimensions, that this method is well def…
Order optimal preconditioners for fully implicit Runge-Kutta schemes applied to the bidomain equations
2010
The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge–Kutta scheme is A-stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one-leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly po…
A note on an overdetermined problem for the capacitary potential
2016
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.