Dr. Aris Marcolongo  Dr. Tobias Binninger  Dr. Federico Zipoli  Dr. Teodoro Laino 《ChemSystemsChem》2020,2(3):e1900031

The recently published DeePMD model, based on a deep neural network architecture, brings the hope of solving the time-scale issue which often prevents the application of first principle molecular dynamics to physical systems. With this contribution we assess the performance of the DeePMD potential on a real-life application and model diffusion of ions in solid-state electrolytes. We consider as test cases the well known Li₁₀GeP₂S₁₂, Li₇La₃Zr₂O₁₂ and Na₃Zr₂Si₂PO₁₂. We develop and test a training protocol suitable for the computation of diffusion coefficients, which is one of the key properties to be optimized for battery applications, and we find good agreement with previous computations. Our results show that the DeePMD model may be a successful component of a framework to identify novel solid-state electrolytes.  相似文献   

    

Fei Zhao  Zhiqiang Sheng  Guangwei Yuan 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2020,100(5):e201900320

We present a novel monotone scheme which is a combination of linear scheme and nonlinear monotone scheme for solving diffusion problems on general polygonal meshes. It will be called as a combination scheme and consists of two steps. Firstly, a second-order accurate linear scheme is used to obtain an approximate solution. Secondly, a nonlinear monotone scheme is used to solve the diffusion equation, where the unknowns in the nonlinear coefficient of the nonlinear monotone scheme are taken as the approximate solution of the linear scheme above, i.e., a linearized monotone scheme is obtained. So the combination scheme does not require nonlinear iterations for solving linear diffusion problems, moreover, it benefits from the accuracy and efficiency of the linear scheme, as well as the monotonicity of nonlinear monotone scheme. We also analyze some properties satisfied by the combination scheme, such as conservation, stability, monotonicity and convergence. Numerical results are presented to show the performance of the monotone combination scheme on distorted meshes, especially some numerical comparisons among our combination scheme with some existing linear and nonlinear monotone schemes are given.  相似文献   

    

Marie-Claude Viallon 《国际流体数值方法杂志》2020,92(5):391-421

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.  相似文献   

    

J. Christy Roja  A. Tamilselvan  N. Geetha 《国际流体数值方法杂志》2020,92(6):528-544

In this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second-order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.  相似文献   

    

F. Gallerano  G. Cannata  F. Lasaponara 《国际流体数值方法杂志》2016,80(10):571-613

In this paper, we propose a model based on a new contravariant integral form of the fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities in the numerical integration of fully nonlinear Boussinesq equation on generalized boundary‐conforming grids is presented. The Boussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme. The proposed high‐order upwind weighted essentially non‐oscillatory finite volume scheme involves an exact Riemann solver and is based on a genuinely two‐dimensional reconstruction procedure, which uses a convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations. The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave‐induced currents is verified against test cases present in the literature. The results obtained are compared with experimental measures, analytical solutions, or alternative numerical solutions. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

    

Xue-song Li  Xin-liang Li 《International Journal of Computational Fluid Dynamics》2016,30(1):69-78

As a type of shock-capturing scheme, the traditional Roe scheme fails in large eddy simulation (LES) because it cannot reproduce important turbulent characteristics, such as the famous k^?5/3 spectral law, as a consequence of the large numerical dissipation. In this work, the Roe scheme is divided into five parts, namely, ξ, δU_p, δp_p, δU_u, and δp_u, which denote basic upwind dissipation, pressure difference-driven modification of interface fluxes, pressure difference-driven modification of pressure, velocity difference-driven modification of interface fluxes, and velocity difference-driven modification of pressure, respectively. Then, the role of each part in the LES of homogeneous decaying turbulence with a low Mach number is investigated. Results show that the parts δU_u, δp_p, and δU_p have little effect on LES. Such minimal effect is integral to computational stability, especially for δU_p. The large numerical dissipation is due to ξ and δp_u, each of which features a larger dissipation than the sub-grid scale model. On the basis of these conditions, an improved all-speed Roe scheme for LES is proposed. This scheme can provide satisfactory LES results even for coarse grid resolutions with usually adopted second-order reconstructions for the finite volume method.  相似文献   

    

Lan Li  Jing An 《Numerical Methods for Partial Differential Equations》2021,37(1):152-171

In this paper, we propose an effective spectral method based on dimension reduction scheme for fourth order problems in polar geometric domains. First, the original problem is decomposed into a series of one‐dimensional fourth order problems by polar coordinate transformation and the orthogonal properties of Fourier basis function. Then the weak form and the corresponding discrete scheme of each one‐dimensional fourth order problem are derived by introducing polar conditions and appropriate weighted Sobolev spaces. In addition, we define the projection operators in the weighted Sobolev space and give its approximation properties, and further prove the error estimation of each one‐dimensional fourth order problem. Finally, we provide some numerical examples, and the numerical results show the effectiveness of our algorithm and the correctness of the theoretical results.  相似文献   

    

Rooji Jinan  Parimal Parag  Himanshu Tyagi 《Entropy (Basel, Switzerland)》2021,23(3)

Samples from a high-dimensional first-order auto-regressive process generated by an independently and identically distributed random innovation sequence are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.  相似文献   

    

Lieneke Kusters  Frans M. J. Willems 《Entropy (Basel, Switzerland)》2021,23(5)

We present a new Multiple-Observations (MO) helper data scheme for secret-key binding to an SRAM-PUF. This MO scheme binds a single key to multiple enrollment observations of the SRAM-PUF. Performance is improved in comparison to classic schemes which generate helper data based on a single enrollment observation. The performance increase can be explained by the fact that the reliabilities of the different SRAM cells are modeled (implicitly) in the helper data. We prove that the scheme achieves secret-key capacity for any number of enrollment observations, and, therefore, it is optimal. We evaluate performance of the scheme using Monte Carlo simulations, where an off-the-shelf LDPC code is used to implement the linear error-correcting code. Another scheme that models the reliabilities of the SRAM cells is the so-called Soft-Decision (SD) helper data scheme. The SD scheme considers the one-probabilities of the SRAM cells as an input, which in practice are not observable. We present a new strategy for the SD scheme that considers the binary SRAM-PUF observations as an input instead and show that the new strategy is optimal and achieves the same reconstruction performance as the MO scheme. Finally, we present a variation on the MO helper data scheme that updates the helper data sequentially after each successful reconstruction of the key. As a result, the error-correcting performance of the scheme is improved over time.  相似文献   

    

Zuojun Zhang  Jiangyu Wang  Mingbo Pu  Xiaoliang Ma  Cheng Huang  Yinghui Guo  Xiangang Luo 《Advanced Optical Materials》2021,9(7):2001736

Transmission–reflection-integrated metasurfaces (TRIMs) provide an effective avenue to realize functionality integration and miniaturization of imaging and communication systems. However, most of the previous works suffer from large chromatic aberrations due to the intrinsic dispersive properties of the resonators constituting metasurfaces, which results in the meta-devices working in a small operation bandwidth. Here, a broadband achromatic TRIM is proposed based on the frequency-multiplexing scheme and dispersion engineering in transmission and reflection mode, respectively. As a proof of the scheme, 1D achromatic transmission–reflection-integrated focusing metasurface and common-caliber transmitarray and reflectarray flat plate antenna are demonstrated over a broad frequency range. The achromatic focusing in transmission mode and reflection mode with simulated focusing efficiencies of 13.12–17.21% and 14.57–20.86% are simultaneously realized at 12–18 and 19–24 GHz, respectively. The radiation gains increase by an average of 17.53 and 23.57 dB for the transmission mode and reflection mode relative to the bare standard rectangle waveguides. The scheme for achromatic and independent electromagnetic manipulation in transmission and reflection mode can also be applied to other frequency ranges and promise unprecedented progress for optical imaging and wireless telecommunication.  相似文献