Search results for "Numerical tests"
showing 10 items of 20 documents
Verifications of Primal Energy Identities for Variational Problems with Obstacles
2018
We discuss error identities for two classes of free boundary problems generated by obstacles. The identities suggest true forms of the respective error measures which consist of two parts: standard energy norm and a certain nonlinear measure. The latter measure controls (in a weak sense) approximation of free boundaries. Numerical tests confirm sharpness of error identities and show that in different examples one or another part of the error measure may be dominant.
A linear approach for the nonlinear distributed parameter identification problem
1991
In identifying the nonlinear distributed parameters we propose an approach, which enables us to identify the nonlinear distributed parameters by just solving linear problems. In this approach we just need to identify linear parameters and then recover the nonlinear parameters from the identified linear parameters. An error estimate for the finite element approximation is derived. Numerical tests are also presented.
Numerical test of finite-size scaling predictions for the droplet condensation-evaporation transition
2016
We numerically study the finite-size droplet condensation-evaporation transition in two dimensions. We consider and compare two orthogonal approaches, namely at fixed temperature and at fixed density, making use of parallel multicanonical simulations. The equivalence between Ising model and lattice gas allows us to compare to analytical predictions. We recover the known background density (at fixed temperature) and transition temperature (at fixed density) in the thermodynamic limit and compare our finite-size deviations to the predicted leading-order finite-size corrections.
Simulations of Array Configurations for the Square Kilometre Array (SKA)
2010
The Square Kilometre Array (SKA) is a new generation radio telescope for the next decades, working at metre to centimetre wavelengths. The SKA will be operational at the same time than other new optical, X-ray and Gamma-ray telescopes. It is of extreme importance that the SKA becomes competitive and complementary to those instruments. An extensive study of technologies and possible configurations involved is needed to ensure the SKA will reach the design specifications. To compare imaging capabilities between different SKA configurations or between the SKA and other instruments, we have implemented figures of merit based on several characteristics of these instruments. In this work we are p…
On the numerical solution of the distributed parameter identification problem
1991
A new error estimate is derived for the numerical identification of a distributed parameter a(x) in a two point boundary value problem, for the case that the finite element method and the fit-to-data output-least-squares technique are used for the identifications. With a special weighted norm, we get a pointwise estimate. Prom the error estimate and also from the numerical tests, we find that if we decrease the mesh size, the maximum error between the identified parameter and the true parameter will increase. In order to improve the accuracy, higher order finite element spaces should be used in the approximations.
Postprocessing of a Finite Element Scheme with Linear Elements
1987
In this contribution we first give a brief survey of postprocessing techniques for accelerating the convergence of finite element schemes for elliptic problems. We also generalize a local superconvergence technique recently analyzed by Křižek and Neittaanmaki ([20]) to a global technique. Finally, we show that it is possible to obtain O(h4) accuracy for the gradient in some cases when only linear elements are used. Numerical tests are presented.
Newton algorithm for Hamiltonian characterization in quantum control
2014
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown paramete…
Inference of Spatiotemporal Processes over Graphs via Kernel Kriged Kalman Filtering
2018
Inference of space-time signals evolving over graphs emerges naturally in a number of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filtering approach that leverages the spatio-temporal dynamics to allow for efficient online reconstruction, while also coping with dynamically evolving network topologies. Laplacian kernels are employed to perform kriging over the graph when spatial second-order statistics are unknown, as is often the case. Numerical tests with synthetic and real data ill…
Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
2016
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
A Continuous Approach to FETI-DP Mortar Methods: Application to Dirichlet and Stokes Problem
2013
In this contribution we extend the FETI-DP mortar method for elliptic problems introduced by Bernardi et al. [2] and Chacon Vera [3] to the case of the incompressible Stokes equations showing that the same results hold in the two dimensional setting. These ideas extend easily to three dimensional problems. Finally some numerical tests are shown as a conclusion. This contribution is a condensed version of a more detailed forthcoming paper. We use standard notation, see for instance [1].