| 1. |
- Asmussen, Sören
(författare)
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A probabilistic look at the Wiener-Hopf equation
- 1998
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Ingår i: SIAM Review. - 0036-1445. ; 40:2, s. 189-201
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Tidskriftsartikel (refereegranskat)abstract
- Existence, uniqueness, and asymptotic properties of solutions Z to the Wiener-Hopf integral equation Z(x) = z(x) + integral(-infinity)(x) Z(x - y)F(dy), x greater than or equal to 0, are discussed by purely probabilistic methods, involving random walks, supermartingales, coupling, the Hewitt-Savage 0-1 law, ladder heights, and exponential change of measure.
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| 2. |
- di Bernardo, M., et al.
(författare)
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Bifurcations in Nonsmooth Dynamical Systems
- 2008
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Ingår i: SIAM Review. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1445 .- 1095-7200. ; 50:4, s. 629-701
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Forskningsöversikt (refereegranskat)abstract
- A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems. Motivated by applications, a pragmatic approach is taken to defining a discontinuity-induced bifurcation (DIB) as a nontrivial interaction of a limit set with respect to a codimension-one discontinuity boundary in phase space. Only DIBs that are local are considered, that is, bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows. Three classes of systems are considered, involving either state jumps, jumps in the vector field, or jumps in some derivative of the vector field. A rich array of dynamics are revealed, involving the sudden creation or disappearance of attractors, jumps to chaos, bifurcation diagrams with sharp corners, and cascades of period adding. For each kind of bifurcation identified, where possible, a kind of "normal form" or discontinuity mapping (DM) is given, together with a canonical example and an application. The goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators, impact oscillators, DC-DC converters, and problems in control theory.
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| 3. |
- Edström, Per
(författare)
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A Fast and Stable Solution Method for the Radiative Transfer Problem
- 2005
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Ingår i: SIAM Review. - 0036-1445 .- 1095-7200. ; 47:3, s. 447-468
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Tidskriftsartikel (refereegranskat)abstract
- Radiative transfer theory considers radiation in turbid media, and is used in a wide range of applications. This paper outlines a problem formulation and a solution method for the radiative transfer problem in multilayer scattering and absorbing media, using discrete ordinate model geometry. A selection of different steps is brought together. The main contribution here is the synthesis of these steps, all of which have been used in different areas, but never all together in one method. First all necessary steps to get a numerically stable solution procedure are treated, and then methods are introduced to increase the speed by a factor of several thousand. This includes methods for handling strongly forward-scattering media. The method is shown to be unconditionally stable, whilst the problem was previously considered numerically intractable.
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| 4. |
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| 5. |
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| 6. |
- Rognes, M.E., et al.
(författare)
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Automated goal-oriented error control i: Stationary variational problems
- 2013
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Ingår i: SIAM Review. - 1095-7200 .- 0036-1445. ; 35:3, s. C173-C193
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Tidskriftsartikel (refereegranskat)abstract
- This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance. Numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented, including Poisson's equation, a mixed formulation of linear elasticity, and the incompressible Navier- Stokes equations. © 2013 Society for Industrial and Applied Mathematics.
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| 7. |
- Shi, Guodong, et al.
(författare)
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Dynamics over Signed Networks
- 2019
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Ingår i: SIAM Review. - : SIAM PUBLICATIONS. - 0036-1445 .- 1095-7200. ; 61:2, s. 229-257
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Tidskriftsartikel (refereegranskat)abstract
- A signed network is a network in which each link is associated with a positive or negative sign. Models for nodes interacting over such signed networks arise from various biological, social, political, and economic systems. As modifications to the conventional DeGroot dynamics for positive links, two basic types of negative interactions along negative links, namely, the opposing rule and the repelling rule, have been proposed and studied in the literature. This paper reviews a few fundamental convergence results for such dynamics over deterministic or random signed networks under a unified algebraic-graphical method. We show that a systematic tool for studying node state evolution over signed networks can be obtained utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions.
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| 8. |
- Thunberg, Hans
(författare)
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Periodicity versus chaos in one-dimensional dynamics
- 2001
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Ingår i: SIAM Review. - 0036-1445 .- 1095-7200. ; 43:1, s. 3-30
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Tidskriftsartikel (refereegranskat)abstract
- We survey recent results in one-dimensional dynamics and, as an application, we derive rigorous basic dynamical facts for two standard models in population dynamics, the Ricker and the Hassell families. We also informally discuss the concept of chaos in the context of one-dimensional discrete time models. First we use the model case of the quadratic family for an informal exposition. We then review precise generic results before turning to the population models. Our focus is on typical asymptotic behavior, seen for most initial conditions and for large sets of maps. Parameter sets corresponding to different types of attractors are described. In particular it is shown that maps with strong chaotic properties appear with positive frequency in parameter space in our population models. Natural measures (asymptotic distributions) and their stability properties are considered.
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| 9. |
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| 10. |
- Wadbro, Eddie, 1981-, et al.
(författare)
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Megapixel topology optimization on a graphics processing unit
- 2009
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Ingår i: SIAM Review. - : Society for Industrial and Applied Mathematics. - 0036-1445 .- 1095-7200. ; 51:4, s. 707-721
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Tidskriftsartikel (refereegranskat)abstract
- We show how the computational power and programmability of modern graphics processing units (GPUs) can be used to efficiently solve large-scale pixel-based material distribution problems using a gradient-based optimality criterion method. To illustrate the principle, a so-called topology optimization problem that results in a constrained nonlinear programming problem with over 4 million decision variables is solved on a commodity GPU.
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| 11. |
- Wahlberg, Bo, 1959-
(författare)
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Orthogonal rational functions : A transformation analysis
- 2003
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Ingår i: SIAM Review. - 0036-1445 .- 1095-7200. ; 45:4, s. 689-705
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Tidskriftsartikel (refereegranskat)abstract
- Finite impulse response (FIR) models are among the most basic tools in control theory and signal processing and are routinely used in almost all fields of application. The connections to orthogonal polynomials are well known. However, infinite impulse response (IIR) models often provide much more compact descriptions and in many cases give improved performance. The objective of this paper is to present a simple framework for the derivation and analysis of orthogonal IIR transfer functions, which are directly related to orthogonal rational functions. Orthogonality simplifies approximation analysis and leads to improved numerical properties. The basic idea is to use a fractional transformation to map the problem to a new domain, where an FIR description is most appropriate. This FIR representation is then mapped back to the original domain to give an orthogonal IIR representation. It is then straightforward to extend many results for FIR. models to IIR model structures with arbitrary stable poles; i.e., properties of orthogonal polynomials are easily generalized to orthogonal rational functions. Much of the theory to be presented is classical, e.g., Laguerre and Kautz functions, and we will make use of well-known results in orthogonal filter theory. However, our main contribution is to present a uniform and transparent theory which also covers more novel results that have mainly been presented in the signals, systems, and control literature in the last decade.
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