The main aim of this paper is to discuss the influence of fractal dimensions on the behavior of the solutions of the Grad-Shafranov equation. Our study is based on the product-like fractal measure ...approach constructed by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal continuum media. The fractal Grad-Shafranov equation gives the possibility to analyze, in a toroidal fusion reactor, the plasma equilibrium in fractal dimensions. Examples of the exact equilibrium solution are given for both the vacuum case outside the plasma and the toroidally shaped spheromak. Note: PACS numbers 05.45.Df: Fractals; 28.52.−s: Fusion reactors; 52.30.Cv: Magnetohydrodynamics; and 52.55.Ip: Spheromaks.
This article presents and studies a two-level grad-div stabilized finite element discretization method for solving numerically the steady incompressible Navier–Stokes equations. The method consists ...of two steps. In the first step, we compute a rough solution by solving a nonlinear Navier–Stokes system on a coarse grid. And then, in the second step, we pass the coarse grid solution to a fine grid to linearize the nonlinear term, update the solution by solving a linearized problem based on Newton iterations. In both steps, a grad-div stabilization term is incorporated into the system to reduce the influence of pressure on the approximate velocity. We analyze stability and asymptotic convergence of the approximate solutions, derive explicit dependence of the solution errors on the grad-div stabilization parameter and viscosity. We perform also some numerical tests to validate the theoretical analysis and illustrate the efficiency of the proposed method. Compared with the standard two-level method without stabilizations, the grad-div stabilization term added in present method improves the accuracy of the approximate velocity, accelerates the convergence of the nonlinear iterations for the coarse mesh nonlinear system, and reduces the computational time.
•A two-level grad-div stabilized finite element discretization method for the incompressible Navier–Stokes equations is presented.•The method is easy to implement based on existing codes.•The method can yield much better solutions than the standard two-level discretization method with reduction in computational time when the viscosity is small.•Convergence results with respective to the mesh size, viscosity and stabilization parameter are derived.•Numerical results demonstrate the promise of the proposed method.
Autori u radu donose preliminarne rezultate arheoloških istraživanja lokaliteta Stari
grad Ljubuški koje je Studij arheologije Filozofskog fakulteta Sveučilišta u Mostaru
proveo u dvije istraživačke ...kampanje, tijekom lipnja 2020. i ožujka 2021. godine. Arheološka
istraživanja i konzervatorsko-restauratorski radovi obavljeni su u okviru dva EU projekta prekograničnih suradnji: FORT-NET i Heritage REVIVED. Iako je riječ o manjim istraživanjima, ona su polučila značajne rezultate koji u mnogome već sada mijenjaju dosadašnje spoznaje, osobito one o vremenu izgradnje i korištenja prostora Staroga grada Ljubuški.
Automatic accent classification is an active research field concerning speech processing. It can be useful to identify a speaker's region of origin, which can be applied in police investigations ...carried out by Law Enforcement Agencies, as well as for the improvement of current speech recognition systems. This paper presents a novel descriptor called Grad-Transfer, extracted using the Gradient-weighted Class Activation Mapping (Grad-CAM) method based on convolutional neural network (CNN) interpretability. Additionally, we propose a methodology for accent classification that implements Grad-Transfer, which is based on transferring the knowledge acquired by a CNN to a classical machine learning algorithm. The paper works on two hypotheses: the coarse localization maps produced by Grad-CAM on spectrograms are able to highlight the regions of the spectrograms that are important for predicting accents, and Grad-Transfer descriptors computed from audios represent distinctive descriptions of the target accents. These hypotheses were demonstrated experimentally, clustering the generated Grad-Transfer descriptors according to the original accent of the audios using Birch and <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-means algorithms. We carried out experiments on the Voice Cloning Toolkit dataset, seeing an increase of macro average accuracy, and unweighted average recall in the results obtained by a Gaussian Naive Bayes classifier up to <inline-formula><tex-math notation="LaTeX">23.00\%</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">23.58\%</tex-math></inline-formula>, respectively, compared to a model trained with spectrograms. This demonstrates that Grad-Transfer is able to improve the performance of accent classification models and opens the door to new implementations in similar tasks.
This work studies a parallel grad-div stabilized finite element algorithm for the damped Stokes equations. In this algorithm, in the light of a fully overlapping domain decomposition technique, we ...solve a global grad-div stabilized problem to compute a local solution in an intersecting subdomain on a global composite mesh, which is fine in the subdomain and rough elsewhere, making the proposed algorithm easy to implement based on an available sequential solver. We derive error bounds of the approximate solutions from our presented algorithm by the theoretical tool of local a priori estimate for the grad-div stabilized finite element solution. Numerical results verify the validity of the theoretical analysis and demonstrate the benefits of the proposed algorithm. On the one hand, compared with the counterpart one excluding grad-div stabilization, this algorithm can reduce significantly the effect of pressure on the approximate velocities, and hence, yields much better approximate velocities in the case of small viscosities. On the other hand, it takes much less computational time in getting approximate solutions with a comparable accuracy than the standard grad-div stabilization method.
PDF
