We present an algebraic version of an iterative multigrid method for obstacle problems,called projected algebraic multigrid(PAMG)here.We show that classical algebraic multigrid algorithms can easily be extended to dea...We present an algebraic version of an iterative multigrid method for obstacle problems,called projected algebraic multigrid(PAMG)here.We show that classical algebraic multigrid 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.展开更多
Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret shari...Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret sharing. Since its introduction, a number of additional applications have been found. This paper contains a detailed exposition of the known results about algebraic manipulation detection codes as well as some new results.展开更多
The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005.The recovery method approximates the solution of the diffusion eq...The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005.The recovery method approximates the solution of the diffusion equation in a discontinuous function space,while inter-element coupling is achieved by a local L_(2)projection that recovers a smooth continuous function underlying the discontinuous approximation.Here we introduce the concept of a local“recovery polynomial basis”–smooth polynomials that are in the weak sense indistinguishable from the discontinuous basis polynomials–and show it allows us to eliminate the recovery procedure.The recovery method reproduces the symmetric discontinuous Galerkin formulation with additional penalty-like terms depending on the targeted accuracy of the method.We present the unique link between the recovery method and discontinuous Galerkin bilinear forms.展开更多
文摘We present an algebraic version of an iterative multigrid method for obstacle problems,called projected algebraic multigrid(PAMG)here.We show that classical algebraic multigrid 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.
基金supported by the Singapore National Research Foundation(Grant No.NRF-CRP2-2007-03)
文摘Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret sharing. Since its introduction, a number of additional applications have been found. This paper contains a detailed exposition of the known results about algebraic manipulation detection codes as well as some new results.
基金Marc van Raalte acknowledges support from the Netherlands Organization for Scientific Research under grant NWO 635.100.009Bram van Leer acknowledges support from the U.S.Air Force Office of Scientific Research under grant FA9950-06-1-0425.
文摘The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005.The recovery method approximates the solution of the diffusion equation in a discontinuous function space,while inter-element coupling is achieved by a local L_(2)projection that recovers a smooth continuous function underlying the discontinuous approximation.Here we introduce the concept of a local“recovery polynomial basis”–smooth polynomials that are in the weak sense indistinguishable from the discontinuous basis polynomials–and show it allows us to eliminate the recovery procedure.The recovery method reproduces the symmetric discontinuous Galerkin formulation with additional penalty-like terms depending on the targeted accuracy of the method.We present the unique link between the recovery method and discontinuous Galerkin bilinear forms.
