查看更多>>摘要：A projected residual algorithm for solving smooth convex optimization problems is presented. The proposed method is an extension of a residual algorithm for solving systems of nonlinear monotone equations introduced by La Cruz (2017), which uses in a systematic way the residual as a search direction combined with the Barzilai-Borwein's choice of the step size and a line search globalization strategy that does not impose the condition that the function value to decrease monotonically at every iteration. The global and R-sublinear convergence of the new method is established. With the aim of showing the advantages of the proposed global scheme an extensive set of numerical experiments including standard test problems and some specific applications are reported. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, the local and parallel two- and three-step backward differentiation formula (BDF2/BDF3) rotational pressure-correction schemes are developed for a coupled Stokes/Darcy system. The central advantage of these schemes is a time-dependent version of domain decomposition by solving the Stokes problem and Darcy problems in their respective domain. By following a similar idea in Guermond et al. (2005), the Stokes problem is solved by a vector-valued elliptic equation and a scalar Poisson equation per time step. The whole system can be composed of three simple linear equations that consume almost the same computational time. Thus, the presented methods can be efficiently applied with less communication requirements and has good parallelism. In theorey, we prove the unconditional stability and long-time stability of the BDF2/BDF3 rotational pressure-correction schemes for the coupled Stokes/Darcy system. Furthermore, some numerical experiments are presented to show the accuracy and efficiency of these schemes in terms of numerical convergence rates and reservoir engineering. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the paper, we present the three-dimensional parallel simulator of tumor progression implemented for GPGPUs, together with an automatic model parameters tuning performed by evolutionary computations. We model the tumor growth by a set of Partial Differential Equations, describing the tumor density, tumor angiogenic factor, and damaged extra-cellular matrix, oxygen concentration, and a couple of auxiliary parameters, tumor pressure, tumor flux, and tumor cell sinks and sources. We also model the changes in the vasculature by the stochastic graph grammar model, expressing the angiogenesis process. We use the finite element method in the isogeometric analysis (IGA) context employing higher-order and continuity B-spline basis functions for approximation of the scalar fields modeling the tumor progression process. We show that replacing the traditional solver algorithm using the loop through elements into the alternative approach employing the loop through global basis functions enables for efficient parallelization on GPGPU. We also employ classical code optimization techniques, includes multithreading organization, memory access, and nesting and unrolling the loops. The experiments performed on the Prometheus supercomputer reported the speed-up of more than 171 times in comparison to analogous CPU simulator for the 256(3) problem size. We also employ the GPGPU code for the solution of an inverse problem of identification of model parameters for patient-specific data. To achieve this goal, we synchronize three different GPGPUs simulators. We use evolutionary algorithms to find a proper model and synchronization parameters matching the prescribed medical data. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider linear scalar wave equations with a hereditary integral term of the kind used to model viscoelastic solids. The kernel in this Volterra integral is a sum of decaying exponentials (The so-called Maxwell, or Zener model) and this allows the introduction of one of two types of families of internal variables, each of which evolve according to an ordinary differential equation (ODE). There is one such ODE for each decaying exponential, and the introduction of these ODEs means that the Volterra integral can be removed from the governing equation. The two types of internal variable are distinguished by whether the unknown appears in the Volterra integral, or whether its time derivative appears; we call the resulting problems the displacement and velocity forms. We define fully discrete formulations for each of these forms by using continuous Galerkin finite element approximations in space and an implicit `Crank-Nicolson' type of finite difference method in time. We prove stability and a priori bounds, and using the FEniCS environment, https://fenicsproject.org/ (The FEniCS project version 1.5, Archive of Numerical Software, 3 (100), 9-23, 2015.) give some numerical results. These bounds do not require Gronwall's inequality and so can be regarded to be of high quality, allowing confidence in long time integration without an a priori exponential build up of error. As far as we are aware this is the first time that these two formulations have been described together with accompanying proofs of such high quality stability and error bounds. The extension of the results to vector-valued viscoelasticity problems is straightforward and summarised at the end. The numerical results are reproducible by acquiring the python sources from https://github.com/Yongseok7717, or by running a custom built docker container (instructions are given). (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper considers a class of non-smooth constrained optimization problems governed by discrete-time nonlinear equations. In these problems, the non-smooth feature comes from the objective function. Our main contributions are as follows. Firstly, by using a smoothing method, the objective function can be approximated by a smooth function, which leads to an approximate optimization problem. Then, based on the idea of l1 penalty function, the state and control constraints are appended to the objective function to form an augmented objective function, which leads to a smooth unconstrained optimization problem. Next, a gradient-based algorithm with a novel line search is proposed for solving this smooth unconstrained optimization problem, and this line search is proved to have a good property similar to the Armijo line search. This is helpful to easily establish convergence results of the proposed algorithm under several mild assumptions. Finally, the proposed algorithm is adopted to solve a long-term hydrothermal optimal scheduling problem, the numerical results show that the proposed algorithm is effective, and the parameter sensitivity analysis results show that the proposed algorithm is also robust.
查看更多>>摘要：In this paper, we present and analyze a space-time weak Galerkin finite element (WG) method for solving the time-dependent symmetric hyperbolic systems. By introducing the discrete weakly differential operator, we construct a stable WG scheme which may be in the local or global form. The local scheme can be solved explicitly, element by element, under certain mesh condition. Then, we establish the stability and derive the optimal L-2-error estimate of O(h(k+1/2))-order for the WG solution when the k-order polynomials are used for k >= 0. Numerical examples are provided to show the effectiveness of the proposed WG method. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we develop a new block triangular preconditioner for solving partial differential equations with random coefficients. We prove spectral bounds for the preconditioned system. Several numerical examples are provided to demonstrate the efficiency of this preconditioner, especially for stochastic problems with large variance. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper aims at proving the convergence and quasi-optimality of an adaptive nonconforming finite element method for Stokes distributed control problems with pointwise control constraints. Nonconforming P-1/P-0 pair (Crouzeix-Raviart elements) and variational discretization are used to approximate the state equation and the control variable, respectively. A posteriori error estimates with upper and lower bounds are first derived for the state and adjoint variables. Then we prove the contraction property for the sum of the energy error of the state and adjoint state and the scaled error estimator on two consecutive adaptive meshes. The resulting linear convergence is finally used to show the quasi-optimal convergence rate of the adaptive algorithm. Additionally, some numerical results are provided to support our theoretical analysis. (c) 2022 Elsevier B.V. All rights reserved.
Shargatov, V. A.Chugainova, A. P.Kolomiytsev, G., V
18页
查看更多>>摘要：We consider traveling wave solutions of generalized Korteweg-de Vries-Burgers equation when the flux function has two inflection points. The dissipation coefficient mu depends only on the spatial coordinate in some moving coordinate system and increases monotonically from mu(1) to mu(2) in the narrow spatial region. Some external influence causes the change in the dissipation coefficient. The set of admissible shocks is defined. In order to determine which discontinuities are admissible, we study the nonlinear (global) stability of traveling wave solutions. Scenarios of the evolution of linearly unstable traveling waves are described, and asymptotics of unstable solutions are found. We find that a stable traveling wave solution and a solution with a time-dependent structure can correspond to the same admissible shock. (c) 2022 Elsevier B.V. All rights reserved.
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Elsevier