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NONLINEAR PROBLEMS
"... Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems ..."
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Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems
Linearity in nonlinear problems
, 2001
"... We study some situations where one encounters a problem which, at first glance, appears to have no solutions at all. But, actually, there is a large linear subspace of solutions of that problem. ..."
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Cited by 15 (0 self)
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We study some situations where one encounters a problem which, at first glance, appears to have no solutions at all. But, actually, there is a large linear subspace of solutions of that problem.
An Improved Particle Filter for Nonlinear Problems
, 2004
"... The Kalman filter provides an effective solution to the linearGaussian filtering problem. However, where there is nonlinearity, either in the model specification or the observation process, other methods are required. We consider methods known generically as particle filters, which include the c ..."
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Cited by 268 (10 self)
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The Kalman filter provides an effective solution to the linearGaussian filtering problem. However, where there is nonlinearity, either in the model specification or the observation process, other methods are required. We consider methods known generically as particle filters, which include
IONED CONJUGATE AND SECANTNEWTON NONLINEAR PROBLEMS
"... The preconditioned conjugate gradient (CG) method is becoming accepted as a powerful tool for solving the linear systems of equations resulting from the application of the finite element method. Applications of the nonlinear algorithm are mainly confined to the diagonally scaled CG. In this study t ..."
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the coupling of preconditioning techniques with nonlinear versions of the conjugate gradient and quasiNewton methods creates a set of conjugate and secantNewton methods for the solution of nonlinear problems. The preconditioning matrices used to improve the ellipticity of the problem and to reduce
Uncertainty quantication in simple linear and nonlinear problems
"... Despite the considerable success of computer simulation technology in science and engineering, it remains dicult to provide objective condence measures of the numerical predictions. This diculty arises from the uncertainties associated with the inputs of any computation attempting to model a physic ..."
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Despite the considerable success of computer simulation technology in science and engineering, it remains dicult to provide objective condence measures of the numerical predictions. This diculty arises from the uncertainties associated with the inputs of any computation attempting to model a physical system. Uncertainties are typically classied as aleatory and epistemic. Aleatory uncertainty (also called variability) arises naturally from randomness in the system, and is studied using probabilistic approaches. The determination of material properties or operating conditions of a physical system typically leads to aleatory uncertainties; additional experimental characterization of such quantities might provide more conclusive evidence and characterization of their variability, but in practical situations it is not possible reduce this type of uncertainty completely. On the other hand, epistemic uncertainty is typically due to incomplete knowledge (or ignorance). This can arise from assumptions introduced in the derivation of the mathematical model or simplications related to the correlation or dependence between physical processes. It is possible to reduce the epistemic uncertainty by using, for example, a combination of calibration, inference from experimental observations, and improvement of
Approximation Techniques for Nonlinear Problems with Continuum of Solutions
 In: Proceedings of The 5th International Symposium on Abstraction, Reformulation and Approximation (SARA’2002
, 2002
"... Most of the working solvers for numerical constraint satisfaction problems (NCSPs) are designed to delivering pointwise solutions with an arbitrary accuracy. When there is a continuum of feasible points this might lead to prohibitively verbose representations of the output. In many practical applic ..."
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Cited by 10 (4 self)
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Most of the working solvers for numerical constraint satisfaction problems (NCSPs) are designed to delivering pointwise solutions with an arbitrary accuracy. When there is a continuum of feasible points this might lead to prohibitively verbose representations of the output. In many practical
PARAMETRIZATION FOR NONLINEAR PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS
"... Abstract. We consider the integral boundaryvalue problem for a certain class of nonlinear systems of ordinary differential equations of the form x ′ (t) = f (t, x (t)) , t ∈ [0, T], ..."
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Abstract. We consider the integral boundaryvalue problem for a certain class of nonlinear systems of ordinary differential equations of the form x ′ (t) = f (t, x (t)) , t ∈ [0, T],
A Variable Local Relaxation Technique in Nonlinear Problems
"... Abstrac t Application of under and overrelaxation is a very useful technique in solution of nonlinear problems. However, the choice of the relaxation factor is problem dependent and difficult to estimate. In this work we propose a new method in which the relaxation factor is chosen automatically ..."
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Abstrac t Application of under and overrelaxation is a very useful technique in solution of nonlinear problems. However, the choice of the relaxation factor is problem dependent and difficult to estimate. In this work we propose a new method in which the relaxation factor is chosen automatically
M.: Asynchronous multidomain variational integrators for nonlinear problems
 International Journal for Numerical Methods in Engineering
"... We develop an asynchronous time integration and coupling method with domain decomposition for linear and nonlinear problems in mechanics. To ensure stability in the time integration and in coupling between domains, we use variational integrators with local Lagrange multipliers to enforce continuity ..."
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Cited by 2 (0 self)
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We develop an asynchronous time integration and coupling method with domain decomposition for linear and nonlinear problems in mechanics. To ensure stability in the time integration and in coupling between domains, we use variational integrators with local Lagrange multipliers to enforce
VERSION OF THE FINITE ELEMENT METHOD FOR PHYSICALLY NONLINEAR PROBLEMS
"... Abstract. In this paper we present an discretization strategy for physically nonlinear problems that is based on a high order finite element formulation. In order to achieve convergence, the version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or ..."
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Abstract. In this paper we present an discretization strategy for physically nonlinear problems that is based on a high order finite element formulation. In order to achieve convergence, the version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally
Results 1  10
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