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Journal articles on the topic 'Method of asymptotic partial domain decomposition'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

PANASENKO, G. P. "METHOD OF ASYMPTOTIC PARTIAL DECOMPOSITION OF DOMAIN." Mathematical Models and Methods in Applied Sciences 08, no. 01 (1998): 139–56. http://dx.doi.org/10.1142/s021820259800007x.

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A new method of partial decomposition of a domain is proposed for partial differential equations, depending on a small parameter. It is based on the information about the structure of the asymptotic solution in different parts of the domain. The principal idea of the method is to extract the subdomain of singular behavior of the solution and to simplify the problem in the subdomain of regular behavior of the solution. The special interface conditions are imposed on the common boundary of these partially decomposed subdomains. If, for example, the domain depends on the small parameter and some

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2

Panasenko, Grigory. "Method of asymptotic partial decomposition of domain for multistructures." Applicable Analysis 96, no. 16 (2016): 2771–79. http://dx.doi.org/10.1080/00036811.2016.1240366.

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3

PANASENKO, GRIGORY. "THE PARTIAL HOMOGENIZATION: CONTINUOUS AND SEMI-DISCRETIZED VERSIONS." Mathematical Models and Methods in Applied Sciences 17, no. 08 (2007): 1183–209. http://dx.doi.org/10.1142/s0218202507002248.

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The partial homogenization is a new method for the treatment of the boundary layers in the homogenization theory. It keeps the initial formulation near the boundary, passes to the high order homogenization at some distance from the boundary and prescribes the asymptotically precise junction conditions between the homogenized and the heterogeneous models at the interface. This method is related to the method of asymptotic partial domain decomposition MAPDD (see G. Panasenko, Method of asymptotic partial decomposition of domain, Math. Mod. Meth. Appl. Sci.8 (1998) 139–156). The partial homogeniz

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4

BLANC, F., O. GIPOULOUX, G. PANASENKO, and A. M. ZINE. "ASYMPTOTIC ANALYSIS AND PARTIAL ASYMPTOTIC DECOMPOSITION OF DOMAIN FOR STOKES EQUATION IN TUBE STRUCTURE." Mathematical Models and Methods in Applied Sciences 09, no. 09 (1999): 1351–78. http://dx.doi.org/10.1142/s0218202599000609.

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The Stokes problem posed in tube structures (or finite rod structures (see Panasenko10)), i.e. in connected finite unions of the thin cylinders with the ratio of the diameter to the height of the order [Formula: see text], is considered. The asymptotic expansion of the solution is built and justified. Boundary layers are studied. Earlier the Navier–Stokes problem in one thin domain was considered by Nazarov.8 The method of asymptotic partial decomposition of the domain (MAPDD) (see Panasenko11) is applied and justified for the Stokes problem posed in a tube structures. This method reduces the

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5

DUPUY, D., G. P. PANASENKO, and R. STAVRE. "ASYMPTOTIC METHODS FOR MICROPOLAR FLUIDS IN A TUBE STRUCTURE." Mathematical Models and Methods in Applied Sciences 14, no. 05 (2004): 735–58. http://dx.doi.org/10.1142/s0218202504003428.

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The steady motion of a micropolar fluid through a wavy tube with the dimensions depending on a small parameter is studied. An asymptotic expansion is proposed and error estimates are proved by using a boundary layer method. We apply the method of partial asymptotic decomposition of domain and we prove that the solution of the partially decomposed problem represents a good approximation for the solution of the considered problem.

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6

Amosov, Andrey, Delfina Gómez, Grigory Panasenko, and Maria-Eugenia Pérez-Martinez. "Asymptotic Domain Decomposition Method for Approximation the Spectrum of the Diffusion Operator in a Domain Containing Thin Tubes." Mathematics 11, no. 16 (2023): 3592. http://dx.doi.org/10.3390/math11163592.

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The spectral problem for the diffusion operator is considered in a domain containing thin tubes. A new version of the method of partial asymptotic decomposition of the domain is introduced to reduce the dimension inside the tubes. It truncates the tubes at some small distance from the ends of the tubes and replaces the tubes with segments. At the interface of the three-dimensional and one-dimensional subdomains, special junction conditions are set: the pointwise continuity of the flux and the continuity of the average over a cross-section of the eigenfunctions. The existence of the discrete sp

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7

Panasenko, G., and M. C. Viallon. "Finite volume implementation of the method of asymptotic partial domain decomposition for the heat equation on a thin structure." Russian Journal of Mathematical Physics 22, no. 2 (2015): 237–63. http://dx.doi.org/10.1134/s1061920815020107.

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8

Appadu, Appanah Rao, and Abey Sherif Kelil. "Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations." Demonstratio Mathematica 54, no. 1 (2021): 377–409. http://dx.doi.org/10.1515/dema-2021-0039.

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Abstract The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of th

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9

Panasenko, G. P., and R. Stavre. "Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow." Mathematical Models and Methods in Applied Sciences 24, no. 09 (2014): 1781–822. http://dx.doi.org/10.1142/s0218202514500079.

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The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid flow–thin elastic plate" when the thickness of the plate, ε, tends to zero, while the density and the Young's modulus of the plate material are of order ε-1and ε-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when ε tends to zero and it is pro

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10

PATERA, ANTHONY T., and EINAR M. RØNQUIST. "A GENERAL OUTPUT BOUND RESULT: APPLICATION TO DISCRETIZATION AND ITERATION ERROR ESTIMATION AND CONTROL." Mathematical Models and Methods in Applied Sciences 11, no. 04 (2001): 685–712. http://dx.doi.org/10.1142/s0218202501001057.

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We present a general adjoint procedure that, under certain hypotheses, provides inexpensive, rigorous, accurate, and constant-free lower and upper asymptotic bounds for the error in "outputs" which are linear functionals of solutions to linear (e.g. partial-differential or algebraic) equations. We describe two particular instantiations for which the necessary hypotheses can be readily verified. The first case — a re-interpretation of earlier work — assesses the error due to discretization: an implicit Neumann-subproblem finite element a posteriori technique applicable to general elliptic parti

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11

Buscaglia, Gustavo C., Jérôme Pousin, and Kamel Slimani. "A posterioriestimate and asymptotic partial domain decomposition." Applicable Analysis 92, no. 12 (2013): 2561–77. http://dx.doi.org/10.1080/00036811.2012.746965.

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12

Nachit, Abdessalem, Gregory P. Panasenko, and Abdelmalek Zine. "ASYMPTOTIC PARTIAL DOMAIN DECOMPOSITION IN THIN TUBE STRUCTURES: NUMERICAL EXPERIMENTS." International Journal for Multiscale Computational Engineering 11, no. 5 (2013): 407–41. http://dx.doi.org/10.1615/intjmultcompeng.2013004259.

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13

Panasenko, G., and M. C. Viallon. "The finite volume implementation of the partial asymptotic domain decomposition." Applicable Analysis 87, no. 12 (2008): 1397–424. http://dx.doi.org/10.1080/00036810802282533.

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14

Panasenko, Grigory, and Marie-Claude Viallon. "Method of asymptotic partial decomposition with discontinuous junctions." Computers & Mathematics with Applications 105 (January 2022): 75–93. http://dx.doi.org/10.1016/j.camwa.2021.11.017.

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15

Gaudiello, Antonio, Grigory Panasenko, and Andrey Piatnitski. "Asymptotic analysis and domain decomposition for a biharmonic problem in a thin multi-structure." Communications in Contemporary Mathematics 18, no. 05 (2016): 1550057. http://dx.doi.org/10.1142/s0219199715500571.

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In the paper, we consider the Dirichlet boundary value problem for the biharmonic equation defined in a thin T-like shaped structure. Our goal is to construct an asymptotic expansion of its solution. We provide error estimates and also introduce and justify the asymptotic partial domain decomposition for this problem.

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16

Panasenko, G. P., and E. Pérez. "Asymptotic partial decomposition of domain for spectral problems in rod structures." Journal de Mathématiques Pures et Appliquées 87, no. 1 (2007): 1–36. http://dx.doi.org/10.1016/j.matpur.2006.10.003.

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17

Panasenko, Grigori P. "Partial asymptotic decomposition of domain: Navier-Stokes equation in tube structure." Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy 326, no. 12 (1998): 893–98. http://dx.doi.org/10.1016/s1251-8069(99)80045-3.

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18

Panasenko, G. P. "Partial asymptotic decomposition of the domain for the diffusion-discrete absorption equation." Proceedings of the Steklov Institute of Mathematics 281, S1 (2013): 118–25. http://dx.doi.org/10.1134/s0081543813050118.

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19

Panasenko, Grigory. "Parallelization of the algorithm of asymptotic partial domain decomposition in thin tube structures." Comptes Rendus Mécanique 338, no. 12 (2010): 675–80. http://dx.doi.org/10.1016/j.crme.2010.10.007.

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20

Panasenko, Grigory, and Marie-Claude Viallon. "Error estimate in a finite volume approximation of the partial asymptotic domain decomposition." Mathematical Methods in the Applied Sciences 36, no. 14 (2013): 1892–917. http://dx.doi.org/10.1002/mma.2735.

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21

Okoubi, Firmin Andzembe, and Jonas Koko. "Parallel Nesterov Domain Decomposition Method for Elliptic Partial Differential Equations." Parallel Processing Letters 30, no. 01 (2020): 2050004. http://dx.doi.org/10.1142/s0129626420500048.

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We study a parallel non-overlapping domain decomposition method, based on the Nesterov accelerated gradient descent, for the numerical approximation of elliptic partial differential equations. The problem is reformulated as a constrained (convex) minimization problem with the interface continuity conditions as constraints. The resulting domain decomposition method is an accelerated projected gradient descent with convergence rate [Formula: see text]. At each iteration, the proposed method needs only one matrix/vector multiplication. Numerical experiments show that significant (standard and sca

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22

Panasenko, Grigori P. "Asymptotic expansion of the solution of navier-stokes equation in tube structure and partial asymptotic decomposition of the domain." Applicable Analysis 76, no. 3-4 (2000): 363–81. http://dx.doi.org/10.1080/00036810008840890.

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23

Bouatta, Mohamed A., Sergey A. Vasilyev, and Sergey I. Vinitsky. "The asymptotic solution of a singularly perturbed Cauchy problem for Fokker-Planck equation." Discrete and Continuous Models and Applied Computational Science 29, no. 2 (2021): 126–45. http://dx.doi.org/10.22363/2658-4670-2021-29-2-126-145.

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The asymptotic method is a very attractive area of applied mathematics. There are many modern research directions which use a small parameter such as statistical mechanics, chemical reaction theory and so on. The application of the Fokker-Planck equation (FPE) with a small parameter is the most popular because this equation is the parabolic partial differential equations and the solutions of FPE give the probability density function. In this paper we investigate the singularly perturbed Cauchy problem for symmetric linear system of parabolic partial differential equations with a small paramete

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24

Li, Ke, Kejun Tang, Tianfan Wu, and Qifeng Liao. "D3M: A Deep Domain Decomposition Method for Partial Differential Equations." IEEE Access 8 (2020): 5283–94. http://dx.doi.org/10.1109/access.2019.2957200.

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25

Gunzburger, M. D., J. S. Peterson, and H. Kwon. "An optimization based domain decomposition method for partial differential equations." Computers & Mathematics with Applications 37, no. 10 (1999): 77–93. http://dx.doi.org/10.1016/s0898-1221(99)00127-3.

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26

Arshad, Muhammad. "Domain decomposition and expanded mixed method for parabolic partial differential equations." Journal of Computational and Applied Mathematics 410 (August 2022): 114183. http://dx.doi.org/10.1016/j.cam.2022.114183.

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27

Gunzburger, M. D., and Jeehyun Lee. "A domain decomposition method for optimization problems for partial differential equations." Computers & Mathematics with Applications 40, no. 2-3 (2000): 177–92. http://dx.doi.org/10.1016/s0898-1221(00)00152-8.

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28

Duan, Y., P. F. Tang, and T. Z. Huang. "A novel domain decomposition method for highly oscillating partial differential equations." Engineering Analysis with Boundary Elements 33, no. 11 (2009): 1284–88. http://dx.doi.org/10.1016/j.enganabound.2009.05.002.

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29

Glizer, Valery Y. "Stability Analysis of Some Types of Singularly Perturbed Time-Delay Differential Systems: Symmetric Matrix Riccati Equation Approach." Symmetry 16, no. 7 (2024): 838. http://dx.doi.org/10.3390/sym16070838.

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Several types of linear and nonlinear singularly perturbed time-delay differential systems are considered. Asymptotic stability of the linear systems and asymptotic stability of the trivial solution of the nonlinear systems, valid for any sufficiently small value of the parameter of singular perturbation, are analyzed. For the stability analysis in the linear case, a partial exact slow–fast decomposition of the original system and an application of the Symmetric Matrix Riccati Equation method are proposed. Such an analysis yields parameter-free conditions, providing the asymptotic stability of

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30

Luo, Wei-Hua, Liang Yin, and Jun Guo. "A modified domain decomposition spectral collocation method for parabolic partial differential equations." Networks and Heterogeneous Media 19, no. 3 (2024): 923–39. http://dx.doi.org/10.3934/nhm.2024041.

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<p>In this paper, utilizing Legendre polynomials as the basis functions in both space and time, we present a modified domain decomposition spectral method for 2-dimensional parabolic partial differential equations. For solving the obtained linear/nonlinear algebraic equations, a dimension expanding preconditioner is applied employing the obtained saddle construction of the coefficient matrix. Numerical examples are given to show the performance of the presented method and the efficiency of the preconditioner.</p>

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31

Rice, J. R., E. A. Vavalis, and Daoqi Yang. "Analysis of a nonoverlapping domain decomposition method for elliptic partial differential equations." Journal of Computational and Applied Mathematics 87, no. 1 (1997): 11–19. http://dx.doi.org/10.1016/s0377-0427(97)00172-6.

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32

Chen, Hai Long, A. Man Zhang, and Shi Li Sun. "The Highly Efficient Calculation Method of 3-D Frequency-Domain Green Function." Key Engineering Materials 419-420 (October 2009): 81–84. http://dx.doi.org/10.4028/www.scientific.net/kem.419-420.81.

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The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation. This method requires very careful divisions of the regions the variables of the integrand. Thus the computing process can be time consuming, which greatly affects the calculation efficiency. Gaussian quadrature is applied to the numerical calculation of the frequency-domain Green function and its partial derivatives. The variation trend of Green function and its partial derivatives along the coordinate plane is analyzed. Comparison of the ca

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33

Fiza, Mehreen, Hakeem Ullah, Saeed Islam, Qayum Shah, Farkhanda Inayat Chohan, and Mustafa Bin Mamat. "Modifications of the Multistep Optimal Homotopy Asymptotic Method to Some Nonlinear KdV-Equations." European Journal of Pure and Applied Mathematics 11, no. 2 (2018): 537–52. http://dx.doi.org/10.29020/nybg.ejpam.v11i2.3194.

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In this article we have introduced the mathematical theory of multistep optimal homotopy asymptotic method (MOHAM). The proposed method is implemented to different models having system of partial differential equations (PDEs). The results obtained by proposed method are compared with Homotopy Analysis Method (HAM) and closed form solutions. The comparisons of these results show that MOHAM is simpler in applicability, effective, explicit, control the convergence through optimal constants, involve less computational work. The MOHAM is independent of the assumption of initial conditions and small

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34

Röst, Gergely, and Jianhong Wu. "Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2086 (2007): 2655–69. http://dx.doi.org/10.1098/rspa.2007.1890.

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The dynamics generated by the delay differential equation with unimodal feedback is studied. The existence of the global attractor is shown and bounds of the attractor are given. We find attractive invariant intervals and give sufficient conditions that guarantee that all solutions enter the domain where f ′ is negative with respect to a positive equilibrium, so the results for delayed monotone feedback can be applied to describe the asymptotic behaviour of solutions. In particular, the existence of heteroclinic orbits from the trivial equilibrium to a periodic orbit oscillating around the pos

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35

C.Y., Wang. "SINGULAR RISE AND SINGULAR DROP OF CUTOFF FREQUENCIES IN SLOT LINE AND STRIP LINE WAVEGUIDES." International Journal of Electromagnetics ( IJEL ) 2, no. 1 (2020): 1 to 16. https://doi.org/10.5281/zenodo.3667104.

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The complete frequency spectrum of the circularly- shielded slot line and strip line are determined using an efficient domain decomposition and mode matching method. Asymptotic analyses show that, when the gap width of the slot line or the width of the strip line are too small, the TE frequencies may drop singularly and the TM frequencies may rise singularly. These new properties greatly affect the cutoff frequencies.

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36

Morrison, John C., Kyle Steffen, Blake Pantoja, Asha Nagaiya, Jacek Kobus, and Thomas Ericsson. "Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules II." Communications in Computational Physics 19, no. 3 (2016): 632–47. http://dx.doi.org/10.4208/cicp.101114.170615a.

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AbstractIn order to solve the partial differential equations that arise in the Hartree- Fock theory for diatomicmolecules and inmolecular theories that include electron correlation, one needs efficient methods for solving partial differential equations. In this article, we present numerical results for a two-variablemodel problem of the kind that arises when one solves the Hartree-Fock equations for a diatomic molecule. We compare results obtained using the spline collocation and domain decomposition methods with third-order Hermite splines to results obtained using the more-established finite

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37

Gunzburger, Max D., Matthias Heinkenschloss, and Hyesuk Kwon Lee. "Solution of elliptic partial differential equations by an optimization-based domain decomposition method." Applied Mathematics and Computation 113, no. 2-3 (2000): 111–39. http://dx.doi.org/10.1016/s0096-3003(99)00076-4.

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38

BERKES, ISTVÁN, LAJOS HORVÁTH, and JOHANNES SCHAUER. "ASYMPTOTIC BEHAVIOR OF TRIMMED SUMS." Stochastics and Dynamics 12, no. 01 (2012): 1150002. http://dx.doi.org/10.1142/s0219493712003602.

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Trimming is a standard method to decrease the effect of large sample elements in statistical procedures, used, e.g., for constructing robust estimators. It is also a powerful tool in understanding deeper properties of partial sums of independent random variables. In this paper we review some basic results of the theory and discuss new results in the central limit theory of trimmed sums. In particular, we show that for random variables in the domain of attraction of a stable law with parameter 0 < α < 2, the asymptotic behavior of modulus trimmed sums depends sensitively on the number of

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39

Wang, Li. "The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions." Advances in Applied Mathematics and Mechanics 4, no. 5 (2012): 603–16. http://dx.doi.org/10.4208/aamm.10-m11159.

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AbstractIn this paper, the collocation methods are used to solve the boundary integral equations of the first kind on the polygon. By means of Sidi’s periodic transformation and domain decomposition, the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers (i = 1,...,d), which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations. Numerical experiments are carried out to show that the methods are very efficient.

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40

Sheng, Lili, Fangyuan Kang, Jianxi Zhao, and Ruiping Liu. "Estimation of A Partial Linear Model with Instrumental Variable for the Longitudinal Data." Journal of Physics: Conference Series 2449, no. 1 (2023): 012011. http://dx.doi.org/10.1088/1742-6596/2449/1/012011.

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Abstract A partial linear model with instrumental variables was developed for longitudinal data. In the partially linear model, the explanatory variable is an endogenous variable, which is correlated with the error term. The endogenous variable was expressed by an instrumental variable and an error item. The endogenous variable was estimated by the instrumental variable through the least square method. B-spline regression combined with QR decomposition was used to approximate the nonparametric function. For the estimation of parametric, the Quadratic inference function and Secant method were a

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41

Jolivet, Pierre, Frédéric Hecht, Frédéric Nataf, and Christophe Prud'homme. "Scalable Domain Decomposition Preconditioners for Heterogeneous Elliptic Problems." Scientific Programming 22, no. 2 (2014): 157–71. http://dx.doi.org/10.1155/2014/268467.

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Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this paper, a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid

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42

Luo, Dong Song, and Kun Peng Chen. "Envelope Signal of Partial Discharge Pattern Recognition Based on Wavelet Packet Transform." Advanced Materials Research 823 (October 2013): 536–40. http://dx.doi.org/10.4028/www.scientific.net/amr.823.536.

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In order to achieve the GIS fault detection and defect type recognition, four typical defect models were designed and discharge tests are carried out aiming at insulation defect as well as discharge characteristics in the GIS .With a large number of ultra high frequency envelope signal ,a method of domain feature extraction was proposed based on wavelet packet transform with singular value decomposition .The envelope signal was decomposed through wavelet packet transform first in the method, then the coefficient matrix of wavelet packet transform was built in the scale ,after that feature vect

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43

Pottosin, Yu V. "A heuristic method for bi-decomposition of partial Boolean functions." Informatics 17, no. 3 (2020): 44–53. http://dx.doi.org/10.37661/1816-0301-2020-17-3-44-53.

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The problem of decomposition of a Boolean function is to represent a given Boolean function in the form of a superposition of some Boolean functions whose number of arguments are less than the number of given function. The bi-decomposition represents a given function as a logic algebra operation, which is also given, over two Boolean functions. The task is reduced to specification of those two functions. A method for bi-decomposition of incompletely specified (partial) Boolean function is suggested. The given Boolean function is specified by two sets, one of which is the part of the Boolean sp

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44

Seo, Jeong-Kweon, and Byeong-Chun Shin. "Reduced-order modeling using the frequency-domain method for parabolic partial differential equations." AIMS Mathematics 8, no. 7 (2023): 15255–68. http://dx.doi.org/10.3934/math.2023779.

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<abstract><p>This paper suggests reduced-order modeling using the Galerkin proper orthogonal decomposition (POD) to find approximate solutions for parabolic partial differential equations. We first transform a parabolic partial differential equation to the frequency-dependent elliptic equations using the Fourier integral transform in time. Such a frequency-domain method enables efficiently implementing a parallel computation to approximate the solutions because the frequency-variable elliptic equations have independent frequencies. Then, we introduce reduced-order modeling to deter

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45

SHI, LEI, and HONGJUN GAO. "BIFURCATION ANALYSIS OF AN AMPLITUDE EQUATION." International Journal of Bifurcation and Chaos 23, no. 05 (2013): 1350081. http://dx.doi.org/10.1142/s0218127413500818.

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We study the bifurcation and stability of constant stationary solutions (u0, v0) of a particular system of parabolic partial differential equations as amplitude equations on a bounded domain (0, L) with Neumann boundary conditions. In this paper, the asymptotic behavior of the solutions (u0, v0) of the amplitude equations are considered. With the length L of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches are studied. We also analyze the stability of the bifurcated solutions.

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46

Savva, Nikos, Danny Groves, and Serafim Kalliadasis. "Droplet dynamics on chemically heterogeneous substrates." Journal of Fluid Mechanics 859 (November 16, 2018): 321–61. http://dx.doi.org/10.1017/jfm.2018.758.

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Slow droplet motion on chemically heterogeneous substrates is considered analytically and numerically. We adopt the long-wave approximation which yields a single partial differential equation for the droplet height in time and space. A matched asymptotic analysis in the limit of nearly circular contact lines and vanishingly small slip lengths yields a reduced model consisting of a set of ordinary differential equations for the evolution of the Fourier harmonics of the contact line. The analytical predictions are found, within the domain of their validity, to be in good agreement with the solut

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47

Zhang, Yi, Fuzhou Liu, Jie Guan, and Yongli Zhu. "Time-frequency Fusion Method via Convolutional Neural Network for Partial Discharge Classification." Journal of Physics: Conference Series 2452, no. 1 (2023): 012014. http://dx.doi.org/10.1088/1742-6596/2452/1/012014.

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Abstract To improve the accuracy of partial discharge (PD) pattern recognition by jointing time-domain (TD) and frequency-domain (FD) information, a time-frequency (TF) fusion method via convolution neural network (CNN) is proposed in this paper. Firstly, PD signals are represented by PD waveform images and transformed into the envelope of variational mode decomposition-based Hilbert marginal spectrum (VHMS). Secondly, a fusion network, FuNet involving a 2-dimensional CNN (2D-CNN), a 1D-CNN, and a multilayer perceptron (MLP), is established to join TF information. In FuNet, the 2D-CNN inputted

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Wu, Yuqi, and Xiao-Chuan Cai. "A Parallel Domain Decomposition Algorithm for Simulating Blood Flow with Incompressible Navier-Stokes Equations with Resistive Boundary Condition." Communications in Computational Physics 11, no. 4 (2012): 1279–99. http://dx.doi.org/10.4208/cicp.060510.150511s.

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AbstractWe introduce and study a parallel domain decomposition algorithm for the simulation of blood flow in compliant arteries using a fully-coupled system of nonlinear partial differential equations consisting of a linear elasticity equation and the incompressible Navier-Stokes equations with a resistive outflow boundary condition. The system is discretized with a finite element method on unstructured moving meshes and solved by a Newton-Krylov algorithm preconditioned with an overlapping restricted additive Schwarz method. The resistive outflow boundary condition plays an interesting role i

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Kumar, Sunil, and B. V. Rathish Kumar. "A Finite Element Domain Decomposition Approximation for a Semilinear Parabolic Singularly Perturbed Differential Equation." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 1 (2017): 41–55. http://dx.doi.org/10.1515/ijnsns-2015-0156.

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AbstractIn this paper, we propose a Monotone Schwarz Iterative Method (MSIM) under the framework of Domain Decomposition Strategy for solving semilinear parabolic singularly perturbed partial differential equations (SPPDEs). A three-step Taylor Galerkin Finite Element (3TGFE) approximation of semilinear parabolic SPPDE is carried out during each of the stages of the MSIM. Appropriate Interface Problems are introduced to update the subdomain boundary conditions in the Monotone Iterative Domain Decomposition (MIDD) method. The convergence of the MIDD method has been established. In addition, the

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50

Bertoglio, Cristobal, David Nolte, Grigory Panasenko, and Konstantinas Pileckas. "Reconstruction of the Pressure in the Method of Asymptotic Partial Decomposition for the Flows in Tube Structures." SIAM Journal on Applied Mathematics 81, no. 5 (2021): 2083–110. http://dx.doi.org/10.1137/20m1388462.

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