Lanczos vectors computed in finite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality One either accepts this loss and takes more steps or re-biorthogonalizes the Lanczos vecto...
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Lanczos vectors computed in finite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality One either accepts this loss and takes more steps or re-biorthogonalizes the Lanczos vectors at each step. Far the symmetric case, there is a compromise approach. This compromise, known as maintaining semiorthogonality, minimizes the cost of reorthogonalization. This paper extends the compromise to the true-sided Lanczos algorithm and justifies the new algorithm. The compromise is called maintaining semiduality. An advantage of maintaining semiduality is that the computed tridiagonal is a perturbation of a matrix that is exactly similar to the appropriate projection of the given matrix onto the computed subspaces. Another benefit is that the simple two-sided Gram-Schmidt procedure is a viable way to correct for loss of duality. A numerical experiment is included in which our Lanczos code is significantly more efficient than Arnoldi's method.
A fundamental problem in scattering theory is to reconstruct the scattered field on a given region from knowledge of the wave on a surface in the far field. A recent methodology which we call point source methods has ...
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ISBN:
(纸本)0780374029
A fundamental problem in scattering theory is to reconstruct the scattered field on a given region from knowledge of the wave on a surface in the far field. A recent methodology which we call point source methods has been developed and applied to the reconstruction of impenetrable obstacles. In this work we present the application of point source methods to the reconstruction of the scattered acoustic field from far field measurements of an unknown penetrable inhomogeneous medium illuminated by a single plane wave.
The aim of the SCEE 2014 conference was to bring together scientistsfrom academia and industry, mathematicians, electrical engineers, computerscientists, and physicists, with the goal of fostering intensive discussion...
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ISBN:
(数字)9783319303994
ISBN:
(纸本)9783319303987;9783319808000
The aim of the SCEE 2014 conference was to bring together scientists
from academia and industry, mathematicians, electrical engineers, computer
scientists, and physicists, with the goal of fostering intensive discussions on
industrially relevant mathematical problems, with an emphasis on the modeling
and numerical simulation of electronic circuits and devices, electromagnetic
fields, and coupled problems. The methodological focus was on model order
reduction anduncertainty quantification.
We describe an effective approach for computing the maximum amplification of the solution norm of linear differential-algebraic systems that arise, in particular, when approximating with respect to space variables the...
We propose a finite-volume tracking method in multiple space dimensions to approximate weak solutions of the hydromechanical equations that allow two-phase behavior. The method relies on a moving mesh ansatz such that...
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In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp...
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In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume *** main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious ***,we present a cell-centered finite volume method to discretize the fictitious domain *** proposed method is numerically validated for different test *** work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.
This paper deals with the simulateneous optimization of a subset O0 of some domain Ω and its complement O1 = Ω \ O0 both considered as separate elastic objects subject to a set of loading scenarios. If one asks for ...
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