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    Wyświetlanie 1-15 z 15
    Tytuł:
    Algebraic approach to domain decomposition
    Autorzy:
    Práger, Milan
    Powiązania:
    https://bibliotekanauki.pl/articles/1361065.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    block matrix
    domain decomposition
    iterative methods
    Opis:
    An iterative procedure containing two parameters for solving linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numerical example is given as an illustration.
    Źródło:
    Banach Center Publications; 1994, 29, 1; 207-214
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Parallel implementation of ray tracing procedure in anisotropic medium
    Autorzy:
    Pieta, A.
    Dwornik, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1933984.pdf
    Data publikacji:
    2012
    Wydawca:
    Politechnika Gdańska
    Tematy:
    ray tracing
    seismic anisotropy
    domain decomposition
    Opis:
    This article describes a parallel implementation of a ray tracing algorithm in a heterogeneous anisotropic geological medium. The shortest path method, which was used for calculations, can give ray path and travel time of seismic wave propagation even for a random and discontinuous velocity field. The high precision required in such calculations was obtained by employing a dense computational grid. This led to a significant increase in the computational effort of the algorithm. The procedure was parallelized using domain decomposition. The results show that the parallel performance of the ray tracing procedure strongly depends on the assumed geological method and differs between media with and without anisotropy of seismic wave propagation.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2012, 16, 1-2; 135-143
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An influence matrix technique for multi-domain solution of the Navier-Stokes equations in a vorticity-streamfunction formulation
    Zastosowanie metody macierzy wpływu w połączeniu z metodą dekompozycji obszaru obliczeniowego do rozwiązania równań Naviera-Stokesa sformułowanych w postaci wirowość-funkcja prądu
    Autorzy:
    Bogusławski, A.
    Kubacki, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/280218.pdf
    Data publikacji:
    2009
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    spectral methods
    domain decomposition method
    influence matrix technique
    Opis:
    The paper presents new multi-domain algorithms based on the influence matrix technique applied together with the non-overlapping iterative domain decomposition method for solution of the incompressible Navier- Stokes equations in vorticity-streamfunction formulation. The spectral Chebyshev collocation method and the influence matrix algorithm are applied for solution of the Stokes problem in each subdomain resulting from time discretization of the Navier-Stokes equations, while the patching conditions (continuity of the solution and continuity of its first order derivative) at the interfaces between subdomains are satisfied using the iterative domain decomposition algorithm.
    W pracy przedstawiono nowy iteracyjny algorytm dekompozycji obszaru obliczeniowego oparty na metodzie macierzy wpływu w zastosowaniu do równań Naviera- -Stokesa dla przepływu czynnika nieściśliwego w sformułowaniu wirowość-funkcja prądu. Spektralna metoda kolokacji wykorzystująca szeregi wielomianów Czebyszewa oraz metoda macierzy wpływu została zastosowana do rozwiązania zagadnienia Stokesa, będącego rezultatem dyskretyzacji równań Naviera-Stokesa w funkcji czasu, w każdym z podobszarów obszaru obliczeniowego, natomiast warunek ciągłości rozwiązania i jego pierwszej pochodnej na powierzchniach rozdziału pomiędzy podobszarami został uzyskany przy pomocy metody iteracyjnej.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2009, 47, 1; 17-40
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions
    Autorzy:
    Krug, Richard
    Leugering, Günter
    Martin, Alexander
    Schmidt, Martin
    Weninger, Dieter
    Powiązania:
    https://bibliotekanauki.pl/articles/2183473.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    time-domain decomposition
    optimal control
    semilinear hyperbolic systems
    convergence
    Opis:
    In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.
    Źródło:
    Control and Cybernetics; 2021, 50, 4; 427--455
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Penalties, Lagrange multipliers and Nitsche mortaring
    Autorzy:
    Grossmann, Christian
    Powiązania:
    https://bibliotekanauki.pl/articles/729228.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    augmented Lagrangian
    penalty method
    domain decomposition
    Nitsche mortaring
    finite elements
    Opis:
    Penalty methods, augmented Lagrangian methods and Nitsche mortaring are well known numerical methods among the specialists in the related areas optimization and finite elements, respectively, but common aspects are rarely available. The aim of the present paper is to describe these methods from a unifying optimization perspective and to highlight some common features of them.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 2; 205-220
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the blowing up solutions of the 4-d general q-Kuramoto-Sivashinsky equation with exponentially “dominated” nonlinearity and singular weight
    Autorzy:
    Baraket, Sami
    Mahdaoui, Safia
    Ouni, Taieb
    Powiązania:
    https://bibliotekanauki.pl/articles/29519212.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    singular limits
    Green’s function
    nonlinearity
    gradient
    nonlinear domain decomposition method
    Opis:
    Let Ω be a bounded domain in $ \mathbb{R}^4 $ with smooth boundary and let $ x^1, x^2, . . . , x^m $ be m-points in Ω. We are concerned with the problem $ \Delta^2 u - H(x, u, D^k u)=\rho^4 \prod_{i=1}^n | x - p_i |^{4 \alpha_i } f(x)g(u), $ where the principal term is the bi-Laplacian operator, $ H(x, u, D^k u)$ is a functional which grows with respect to $ Du $ at most like $ |Du|^q, 1 ≤ q ≤ 4, f : Ω → [0,+∞[ $ is a smooth function satisfying f(pi) > 0 for any i = 1, . . . , n, $ α_i $ are positives numbers and $ g : \mathbb{R} → [0,+∞[ $ satisfy $ |g(u)| ≤ ce^u $. In this paper, we give sufficient conditions for existence of a family of positive weak solutions $ (u_ρ)_{ρ>0} $ in Ω under Navier boundary conditions u = Δu = 0 on ∂Ω. The solutions we constructed are singular as the parameters ρ tends to 0, when the set of concentration $ S = {x^1, . . . , x^m} ⊂ Ω $ and the set $ Λ := {p_1, . . . , p_n} ⊂ Ω $ are not necessarily disjoint. The proof is mainly based on nonlinear domain decomposition method.
    Źródło:
    Opuscula Mathematica; 2023, 43, 1; 5-18
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Domain decomposition in exact controllability of second order hyperbolic systems on 1-d networks
    Autorzy:
    Lagnese, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205985.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    domain decomposition
    exact controllability
    one-dimensional networks
    second order hyperbolic systems
    Opis:
    This paper is concerned with domain decomposition in exact controllability of a class of linear second order hyperbolic systems on one-dimensional graphs in [R^3] that in particular serve as descriptive models of the dynamics of various multi-link structures consisting of one-dimensional elements, such as networks of Timoshenko beams in [R^3]. We first consider a standard unconstrained optimal control problem in which the cost functional penalizes the deviation of the final state of the global problem from a given target state. A convergent domain decomposition for the optimality system associated with this problem was recently given by G. Leugering. This decomposition depends on the penalty parameter. On each edge of the graph and at each iteration level the local problem is itself the optimality system associated with an unconstrained optimal control problem in which the cost functional penalizes the deviation of the final state of the particular edge from the target state for that edge. The main purpose of this paper is to show that at each iteration level and on each edge the local optimality system converges as the penalty parameter approaches its limit and that the limit system is a domain decomposition for the problem of norm minimum exact control to the target state.
    Źródło:
    Control and Cybernetics; 1999, 28, 3; 531-556
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas flow in networks
    Autorzy:
    Leugering, G.
    Martin, A.
    Schmidt, M.
    Sirvent, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/205527.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    gas networks
    Euler equation
    semilinear PDE
    nonoverlapping domain decomposition
    Opis:
    We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs—ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.
    Źródło:
    Control and Cybernetics; 2017, 46, 3; 191-225
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dirichlet/Dirichlet and Dirichlet/Dirichlet-Neumann/Neumann non-overlapping iterative domain decomposition methods
    Autorzy:
    Kubacki, S.
    Bogusławski, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1933184.pdf
    Data publikacji:
    2008
    Wydawca:
    Politechnika Gdańska
    Tematy:
    non-overlapping domain decomposition method
    parallel computing
    spectral methods
    Helmholtz equation
    Opis:
    A new iterative non-overlapping domain decomposition method is proposed for solving the one- and two-dimensional Helmholtz equation on parallel computers. The spectral collocation method is applied to solve the Helmholtz equation in each subdomain based on the Chebyshev approximation, while the patching conditions are imposed at the interfaces between subdomains through a correction, being a linear function of the space coordinates. Convergence analysis is performed for two applications of the proposed method (DDLC and DDNNLC algorithms - the meaning of these abbreviations is explained below) based on the works of Zanolli and Funaro et al. Numerical tests have been performed and results obtained using the proposed method and other iterative algorithms have been compared. Parallel performance of the multi-domain algorithms has been analyzed by decomposing the two-dimensional domain into a number of subdomains in one spatial direction. For the one-dimensional problem, convergence of the iteration process was quickly obtained using the proposed method, setting a small value of the ? constant in the Helmholtz equation. Another application of the proposed method may be an alternative to other iterative schemes when solving the two-dimensional Helmholtz equation.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2008, 12, 1-2; 85-104
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    3D Multi-Domain MFS Analysis of Sound Pressure Level Reduction Between Connected Enclosures
    Autorzy:
    Godinho, L.
    Branco, F. G.
    Mendes P., A.
    Powiązania:
    https://bibliotekanauki.pl/articles/177013.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Method of Fundamental Solutions (MFS)
    domain decomposition
    closed spaces
    sound pressure level reduction
    Opis:
    In this paper, the authors study the 3D propagation of sound waves between two closed spaces. The separation element between the two rooms is considered to include either a small opening or a homogeneous lightweight panel, coupling the two spaces. A numerical study of this configuration is performed, trying to understand the influence of the position and geometry of this opening in the sound pressure level reduction curve at low and midfrequencies. Additionally, the coupling effect between the two acoustic spaces is analyzed, in order to better understand its importance when determining the sound pressure level reduction. Different boundary conditions are ascribed to the walls of these rooms, simulating both the completely reflecting and partially absorbing surfaces. The numerical modelling was performed using a multi-domain formulation of the Method of Fundamental Solutions (MFS). The system is composed of two coupled rooms, limited by rigid or by absorbing walls, and separated by a thin wall (tending to null thickness) with a small opening. An experimental validation of the proposed model is presented, comparing its results with those found experimentally for a reduced-scale model. It is important to note that, for such a configuration, a traditional single-domain approach using methods like the MFS or the BEM would lead to undetermined equation systems, and thus the proposed model makes use of a domain decomposition technique.
    Źródło:
    Archives of Acoustics; 2011, 36, 3; 575-601
    0137-5075
    Pojawia się w:
    Archives of Acoustics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids
    Autorzy:
    Bresch, D.
    Koko, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/908383.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dwoistość
    gradient sprzężony
    przepływ Naviera-Stokesa
    domain decomposition
    duality
    conjugate gradient
    Navier-Stokes flows
    Opis:
    We present a numerical simulation of two coupled Navier-Stokes flows, using operator-splitting and optimization-based nonoverlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid in rest.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 4; 419-429
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some remarks on the concept of stream tubes for numerical simulations of complex fluid flows - applications
    Autorzy:
    Clermont, J.
    Normandin, M.
    Radu, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206139.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    lepkosprężystość
    linia prądu
    przekształcenie
    symulacja numeryczna
    constitutive equations
    domain decomposition
    incompressible fluid
    stream tubes
    streamlines
    transformations
    viscoelasticity
    Opis:
    This paper presents new theoretical elements for numerical simulation of two- and three-dimensional flows, based on the concept of streamlines and domain decomposition. The so-called "stream-tube method", considered previously particularly for flows inolving open streamlines, is extended to general streamline comfigurations. It is shown how local transformation functions may be defined in order to simulate flows of complex fluids, notably those requiring evaluation of particle time history. The specific features (for example : mass conservation, simplicity in handling time-dependent constitutive equations) of the stream-tube methods previously investigated numerically are still preserved in the new formulation. An example of calculations is given in the case of the two-dimensional flow of a Newtonian fluid between two eccentric cylinders where results are found to be consistent with literature data.
    Źródło:
    Control and Cybernetics; 2000, 29, 2; 535-553
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the convergence of domain decomposition algorithm for the body with thin inclusion
    Autorzy:
    Styahar, A.
    Savula, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/386798.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    elasticity theory
    Timoshenko shell theory
    Steklov-Poincare operator
    domain decomposition
    teoria sprężystości
    teoria Tymoszenki
    operator Steklova-Poincare'a
    Opis:
    We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.
    Źródło:
    Acta Mechanica et Automatica; 2015, 9, 1; 27-32
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of patch substructuring methods
    Autorzy:
    Gander, M. J.
    Halpern, L.
    Magoules, F.
    Roux, F. X.
    Powiązania:
    https://bibliotekanauki.pl/articles/929707.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda rozkładu
    metoda dopełniacza Schura
    zoptymalizowana metoda Schwarza
    Schwarz domain decomposition methods
    Schur complement methods
    patch substructuring methods
    optimized Schwarz methods
    Opis:
    Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains, condensated on the interfaces, to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergence rate than both the algebraic and the geometric one. We complement our results by numerical experiments.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 395-402
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finding robust transfer features for unsupervised domain adaptation
    Autorzy:
    Gao, Depeng
    Wu, Rui
    Liu, Jiafeng
    Fan, Xiaopeng
    Tang, Xianglong
    Powiązania:
    https://bibliotekanauki.pl/articles/331356.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    unsupervised domain adaptation
    feature reduction
    generalized eigenvalue decomposition
    object recognition
    adaptacja domeny
    redukcja cech
    rozkład wartości własnych
    rozpoznawanie obiektu
    Opis:
    An insufficient number or lack of training samples is a bottleneck in traditional machine learning and object recognition. Recently, unsupervised domain adaptation has been proposed and then widely applied for cross-domain object recognition, which can utilize the labeled samples from a source domain to improve the classification performance in a target domain where no labeled sample is available. The two domains have the same feature and label spaces but different distributions. Most existing approaches aim to learn new representations of samples in source and target domains by reducing the distribution discrepancy between domains while maximizing the covariance of all samples. However, they ignore subspace discrimination, which is essential for classification. Recently, some approaches have incorporated discriminative information of source samples, but the learned space tends to be overfitted on these samples, because they do not consider the structure information of target samples. Therefore, we propose a feature reduction approach to learn robust transfer features for reducing the distribution discrepancy between domains and preserving discriminative information of the source domain and the local structure of the target domain. Experimental results on several well-known cross-domain datasets show that the proposed method outperforms state-of-the-art techniques in most cases.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 1; 99-112
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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