Calcolo最新文献

This note discusses the computation of the distance function with respect to Finsler metrics. To this end, we show how the Finsler variants of the Eikonal equation can be solved by a primal-dual algorithm exploiting the variational structure. We also discuss the acceleration of the algorithm by preconditioning techniques, and illustrate the flexibility of the proposed method through a series of numerical examples.

This paper presents ConvStabNet, a convolutional neural network designed to predict optimal stabilization parameters for each cell in the Streamline Upwind Petrov Galerkin (SUPG) stabilization scheme. ConvStabNet employs a shared parameter approach, allowing the network to understand the relationships between cell characteristics and their corresponding stabilization parameters while efficiently handling the parameter space. Comparative analyses with state-of-the-art neural network solvers based on variational formulations highlight the superior performance of ConvStabNet. To improve the accuracy of SUPG in solving partial differential equations (PDEs) with interior and boundary layers, ConvStabNet incorporates a loss function that combines a strong residual component with a cross-wind derivative term. The findings confirm ConvStabNet as a promising method for accurately predicting stabilization parameters in SUPG, thereby marking it as an advancement over neural network-based PDE solvers.

We present a simple yet efficient two-stage extended Kaczmarz-type algorithm for solving large least squares problem. During each stage, the current iterate is projected onto a surrogate hyperplane instead of a single one, yielding remarkable reduction in the number of iteration steps and computational time. We prove that the proposed algorithm converges to the unique least-norm least-squares solution with a convergence factor asymptotically smaller than that for some existing randomized extended Kaczmarz-type algorithms. Numerical examples show that the new algorithm outperforms several counterparts for various test problems.

This work considers the numerical analysis of nonlinear Volterra integrodifferential equations that arise from, e.g., the theory of isotropic viscoelastic rods and plates. Novel properties of the kernel and its derivatives are derived via the Laplace transform, and the regularity of the solutions is proved. Then we apply the Crank–Nicolson method and the second-order convolution quadrature rule to develop the discrete-in-time scheme, and the energy argument is employed to analyze the stability and convergence of the proposed scheme. Numerical experiments are performed to substantiate the theoretical findings.

The (C^1)-(P_{k+1}) ((kge 4)) Argyris finite elements combined with the (C^0)-(P_k) Lagrange finite elements are locking-free with respect to the plate thickness, and quasi-optimal when solving the Reissner–Mindlin plate equation on triangular meshes. The method is truly conforming or consistent in the sense that no reduction operator is introduced to the formulation. Theoretical proof and numerical verification are presented.

In this manuscript, we aim to study the semi-analytical and the numerical solution of a semilinear time-fractional diffusion equation where the time-fractional term includes the combination of tempered fractional derivative and k-Caputo fractional derivative with a parameter (k ge 1). The application of the new integral transform, namely Elzaki transform of the tempered k-Caputo fractional derivative is shown here and thereafter the semi-analytical solution is obtained by using the Elzaki decomposition method. The model problem is linearized using Newton’s quasilinearization method, and then the quasilinearized problem is discretized by the difference scheme namely tempered (_kL2)-(1_sigma ) method. Stability and convergence analysis of the proposed scheme have been discussed in the (L_2)-norm using the energy method. In support of the theoretical results, numerical example has been incorporated.

In this paper, we study the lower and upper bounds for Stokes eigenvalues by finite element schemes. For the schemes studied here, roughly speaking, the loss of the local approximation property of the discrete velocity and pressure spaces may lead to different computed bounds of the eigenvalues. Formally theoretical analysis is constructed based on certain mathematical hypotheses, and numerical experiments are given to illustrate the validity of the theory.

We present an algorithm for Tchakaloff-like compression of quasi-Monte Carlo volume and surface integration on an arbitrary union of balls, via non-negative least squares. We also provide the corresponding Matlab codes together with several numerical tests.

In this study, we investigate a hybrid-type anisotropic weakly over-penalised symmetric interior penalty method for the Poisson equation on convex domains. Compared with the well-known hybrid discontinuous Galerkin methods, our approach is simple and easy to implement. Our primary contributions are the proposal of a new scheme and the demonstration of a proof for the consistency term, which allows us to estimate the anisotropic consistency error. The key idea of the proof is to apply the relation between the Raviart–Thomas finite element space and a discontinuous space. In numerical experiments, we compare the calculation results for standard and anisotropic mesh partitions.

In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and (L^1) data. To deal with the non-coercive character of the equation and the low regularity of the right hand-side we mix the finite volume tools and the renormalized techniques. To handle the Neumann boundary conditions we choose solutions having a null median and we prove a convergence result. We present also some numerical experiments in dimension 2 to illustrate the rate of convergence.