Journal•ISSN: 0885-7474

# Journal of Scientific Computing

Springer Science+Business Media

About: Journal of Scientific Computing is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Finite element method & Discretization. It has an ISSN identifier of 0885-7474. Over the lifetime, 3604 publications have been published receiving 87289 citations.

Topics: Finite element method, Discretization, Mathematics, Discontinuous Galerkin method, Computer science

##### Papers published on a yearly basis

##### Papers

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TL;DR: In this article, a dynamic renormalization group (RNG) method for hydrodynamic turbulence was developed, which uses dynamic scaling and invariance together with iterated perturbation methods, allowing us to evaluate transport coefficients and transport equations for the large scale (slow) modes.

Abstract: We develop the dynamic renormalization group (RNG) method for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, allows us to evaluate transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrumCK=1.617; turbulent Prandtl number for high-Reynolds-number heat transferPt=0.7179; Batchelor constantBa=1.161; and skewness factor¯S3=0.4878. A differentialK-\(\bar \varepsilon \) model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/\(\bar \varepsilon \), decay of isotropic turbulence asK=O(t−1.3307), and the von Karman constantκ=0.372. A differential transport model, based on differential relations betweenK,\(\bar \varepsilon \), andν, is derived that is not divergent whenK→ 0 and\(\bar \varepsilon \) is finite. This latter model is particularly useful near walls.

3,342 citations

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TL;DR: The purpose of the last three sections is to demonstrate by representative examples that control theory can be used to formulate computationally feasible procedures for aerodynamic design, Provided, therefore, that one can afford the cost of a moderate number of flow solutions.

Abstract: The purpose of the last three sections is to demonstrate by representative examples that control theory can be used to formulate computationally feasible procedures for aerodynamic design. The cost of each iteration is of the same order as two flow solutions, since the adjoint equation is of comparable complexity to the flow equation, and the remaining auxiliary equations could be solved quite inexpensively. Provided, therefore, that one can afford the cost of a moderate number of flow solutions, procedures of this type can be used to derive improved designs. The approach is quite general, not limited to particular choices of the coordinate transformation or cost function, which might in fact contain measures of other criteria of performance such as lift and drag. For the sake of simplicity certain complicating factors, such as the need to include a special term in the mapping function to generate a corner at the trailing edge, have been suppressed from the present analysis. Also it remains to explore the numerical implementation of the design procedures proposed in this paper.

1,912 citations

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TL;DR: In this paper, the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function is analyzed, subject to coupled linear equality constraints.

Abstract: In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, $$\phi (x_0,\ldots ,x_p,y)$$
, subject to coupled linear equality constraints. Our ADMM updates each of the primal variables $$x_0,\ldots ,x_p,y$$
, followed by updating the dual variable. We separate the variable y from $$x_i$$
’s as it has a special role in our analysis. The developed convergence guarantee covers a variety of nonconvex functions such as piecewise linear functions, $$\ell _q$$
quasi-norm, Schatten-q quasi-norm (
$$0

867 citations

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TL;DR: This paper shows that global linear convergence can be guaranteed under the assumptions of strong convexity and Lipschitz gradient on one of the two functions, along with certain rank assumptions on A and B.

Abstract: The formulation $$\begin{aligned} \min _{x,y} ~f(x)+g(y),\quad \text{ subject } \text{ to } Ax+By=b, \end{aligned}$$minx,yf(x)+g(y),subjecttoAx+By=b,where f and g are extended-value convex functions, arises in many application areas such as signal processing, imaging and image processing, statistics, and machine learning either naturally or after variable splitting. In many common problems, one of the two objective functions is strictly convex and has Lipschitz continuous gradient. On this kind of problem, a very effective approach is the alternating direction method of multipliers (ADM or ADMM), which solves a sequence of f/g-decoupled subproblems. However, its effectiveness has not been matched by a provably fast rate of convergence; only sublinear rates such as O(1 / k) and $$O(1/k^2)$$O(1/k2) were recently established in the literature, though the O(1 / k) rates do not require strong convexity. This paper shows that global linear convergence can be guaranteed under the assumptions of strong convexity and Lipschitz gradient on one of the two functions, along with certain rank assumptions on A and B. The result applies to various generalizations of ADM that allow the subproblems to be solved faster and less exactly in certain manners. The derived rate of convergence also provides some theoretical guidance for optimizing the ADM parameters. In addition, this paper makes meaningful extensions to the existing global convergence theory of ADM generalizations.

734 citations

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TL;DR: This paper decomposes a given (possible textured) image f into a sum of two functions u+v, where u∈BV is a function of bounded variation (a cartoon or sketchy approximation of f), while v is afunction representing the texture or noise.

Abstract: This paper is devoted to the modeling of real textured images by functional minimization and partial differential equations. Following the ideas of Yves Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, we decompose a given (possible textured) image f into a sum of two functions u+v, where u∈BV is a function of bounded variation (a cartoon or sketchy approximation of f), while v is a function representing the texture or noise. To model v we use the space of oscillating functions introduced by Yves Meyer, which is in some sense the dual of the BV space. The new algorithm is very simple, making use of differential equations and is easily solved in practice. Finally, we implement the method by finite differences, and we present various numerical results on real textured images, showing the obtained decomposition u+v, but we also show how the method can be used for texture discrimination and texture segmentation.

732 citations