A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite...
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A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional(2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.
By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod func...
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By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.
In geologically complex regions, the prestack depth migration is necessary in order to obtain accurate structure images. In this report, we discuss the prestack depth migration by finite-difference (FD) method and Fou...
A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of ...
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A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes.
Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finit...
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Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finite-dim ensionalsubspaces,a stabilization form ulation is pre- sented for the Stokes problem by em ploying nonconform ing elem *** form ulation is uni- form ly coercive and notsubject to the Babus ka-Brezzicondition,and the resulted linear algebraic system is positive definitew ith the spectralcondition num berO(h- 2 ). Quasi-optim alerrorbounds are obtained,which is consistentwith the interpola- tion properties ofthe finite elem entsused.
The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relax...
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The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relaxation methods really have considerably larger convergence domains.
Abstract In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high speed multiprocessor systems is set *** class of methods not only...
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Abstract In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high speed multiprocessor systems is set *** class of methods not only includes all the existing relaxation methods for the linear complementarity problems,but also yields a lot of novel ones in the sense of *** establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H matrix with positive diagonal elements.
It is common engineering practice to use response surface approximations as surrogates for an expensive objective function in engineering design. The rationale is to reduce the number of detailed, costly analyses requ...
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In this paper, we consider the optimization method for monotone variational inequality problems on polyhedral sets. First, we consider the mixed complementarity problem based on the original problem. Then, a merit fun...
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In this paper, we consider the optimization method for monotone variational inequality problems on polyhedral sets. First, we consider the mixed complementarity problem based on the original problem. Then, a merit function for the mixed complementarity problem is proposed and some desirable properties of the merit function are obtained. Under certain assumptions: we show that any stationary point of the merit function is a solution of the original problem. A descent method for the optimization problem is proposed and the global convergence of the method is shown.
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