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436,665
FirstOrder System Least Squares For The StressDisplacement Formulation: Linear Elasticity
 SIAM J. Numer. Anal
, 2003
"... This paper develops a leastsquares nite element method for linear elasticity in both two and three dimensions. The leastsquares functional is based on the stressdisplacement formulation with the symmetry condition of the stress tensor imposed in the firstorder system. For the respective displace ..."
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Cited by 13 (8 self)
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This paper develops a leastsquares nite element method for linear elasticity in both two and three dimensions. The leastsquares functional is based on the stressdisplacement formulation with the symmetry condition of the stress tensor imposed in the firstorder system. For the respective
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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gradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
Mixed Finite Elements for Elasticity in the StressDisplacement Formulation
 CONTEMPORARY MATHEMATICS
"... We present a family of pairs of finite element spaces for the unaltered Hellingerâ€“Reissner variational principle using polynomial shape functions on a single triangular mesh for stress and displacement. There is a member of the family for each polynomial degree, beginning with degree two for the str ..."
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Cited by 3 (0 self)
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for the stress and degree one for the displacement, and each is stable and affords optimal order approximation. The simplest element pair involves 24 local degrees of freedom for the stress and 6 for the displacement. We also construct a lower order element involving 21 stress degrees of freedom and 3
FirstOrder System Least Squares For The Stokes Equations, With Application To Linear Elasticity
 SIAM J. Numer. Anal
"... . Following our earlier work on general secondorder scalar equations, here we develop a leastsquares functional for the two and threedimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated cu ..."
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Cited by 58 (21 self)
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and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressureperturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity, with estimates
An Adaptive Least Squares Mixed Finite Element Method For The StressDisplacement Formulation Of Linear Elasticity
 SIAM Journal on Numerical Analysis
, 2005
"... A leastsquares mixed finite element method for linear elasticity, based on a stressdisplacement formulation, is investigated in terms of computational efficiency. For the stress approximation quadratic RaviartThomas elements are used and these are coupled with the quadratic nonconforming finite ..."
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Cited by 12 (3 self)
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A leastsquares mixed finite element method for linear elasticity, based on a stressdisplacement formulation, is investigated in terms of computational efficiency. For the stress approximation quadratic RaviartThomas elements are used and these are coupled with the quadratic nonconforming finite
Benchmarking Least Squares Support Vector Machine Classifiers
 NEURAL PROCESSING LETTERS
, 2001
"... In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set of eq ..."
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Cited by 446 (46 self)
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In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 435 (20 self)
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In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
FirstOrder System Least Squares for Linear Elasticity: Numerical Results
"... . The aim here is to study two firstorder system leastsquares (FOSLS) methods applied to various boundary value problems of planar linear elasticity. Both use finite element discretization and multigrid solution methods. They are twostage algorithms that first solve for the displacement flux vari ..."
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Cited by 6 (3 self)
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. The aim here is to study two firstorder system leastsquares (FOSLS) methods applied to various boundary value problems of planar linear elasticity. Both use finite element discretization and multigrid solution methods. They are twostage algorithms that first solve for the displacement flux
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
 SIAM J. SCI. STAT. COMPUT
, 1986
"... We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2orthogonal basis of Krylov subspaces. It can be considered a ..."
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Cited by 2046 (40 self)
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We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2orthogonal basis of Krylov subspaces. It can be considered
Fronts propagating with curvature dependent speed: algorithms based on Hamiltonâ€“Jacobi formulations
 Journal of Computational Physics
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1183 (64 self)
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, which resemble HamiltonJacobi equations with parabolic righthandsides, by using techniques from the hyperbolic conservation laws. Nonoscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps
Results 1  10
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436,665