Coelho, D. L.Vitral, E.Pontes, J.Mangiavacchi, N....
20页
查看更多>>摘要：Computational modeling of pattern formation in nonequilibrium systems is a fundamental tool for studying complex phenomena in biology, chemistry, materials and engineering sciences. The pursuit for theoretical descriptions of some among those physical problems led to the Swift-Hohenberg equation (SH3) which describes pattern selection in the vicinity of instabilities. A finite differences scheme, known as Stabilizing Correction (Christov and Pontes, 2002), developed to integrate the cubic Swift-Hohenberg equation in two dimensions, is reviewed and extended in the present paper. The original scheme features Generalized Dirichlet boundary conditions (GDBC), forcings with a spatial ramp of the control parameter, strict implementation of the associated Lyapunov functional, and second-order representation of all derivatives. We now extend these results by including periodic boundary conditions (PBC), forcings with Gaussian distributions of the control parameter and the quintic Swift-Hohenberg (SH35) model. The present scheme also features a strict implementation of the functional for all test cases. A code verification was accomplished, showing unconditional stability, along with second-order accuracy in both time and space. Test cases confirmed the monotonic decay of the Lyapunov functional and all numerical experiments exhibit the main physical features: highly nonlinear behavior, wavelength filter and competition between bulk and boundary effects. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
Caravantes, J.Diaz-Toca, G. M.Fioravanti, M.Gonzalez-Vega, L....
19页
查看更多>>摘要：The problem of detecting when two moving ellipses or ellipsoids overlap is of interest to robotics, CAD/CAM, computer animation, etc., where ellipses and ellipsoids are often used for modelling (and/or enclosing) the shape of the objects under consideration. By analysing symbolically the sign of the real roots of the characteristic polynomial of the pencil defined by two ellipses/ellipsoids A and B given by X(T)AX = 0 and (XBX)-B-T = 0, we derive new formulae characterising when A and B overlap, are separate, or touch each other externally. This characterisation is defined by a minimal set of polynomial inequalities depending only on the entries of A and B so that we need only compute the characteristic polynomial of the pencil defined by A and B, det(TA+B), and not the intersection points between them. Compared with the best available approach dealing with this problem, the new formulae involve a smaller set of polynomials and less sign conditions. As an application, this characterisation provides also a new approach for exact collision detection of two moving ellipses or ellipsoids since the analysis of the univariate polynomials (depending on the time) in the previously mentioned formulae provides the collision events between them.(C) 2021 Elsevier B.V. All rights reserved.
Bentbib, A. H.Jbilou, K.Reichel, L.El Ghomari, M....
18页
查看更多>>摘要：This paper describes methods based on the extended symmetric block Lanczos process for computing element-wise estimates of upper and lower bounds for matrix functions of the form V(T)f (A)V, where the matrix A is an element of R-nxn is large, symmetric, and nonsingular, V is an element of R-nxs is a block vector with 1 < s & laquo;& nbsp;& nbsp;n orthonormal columns, and f is a function that is defined on the convex hull of the spectrum of A. Pairs of block Gauss-Laurent and block anti-Gauss-Laurent quadrature rules are defined and applied to determine the desired estimates. The methods presented generalize methods discussed by Fenu et al. (2013), which use (standard) block Krylov subspaces, to allow the application of extended block Krylov subspaces. The latter spaces are the union of a (standard) block Krylov subspace determined by positive powers of A and a block Krylov subspace defined by negative powers of A. Computed examples illustrate the effectiveness of the proposed method. (C) 2021 Elsevier B.V. All rights reserved.
Waziri, Mohammed YusufAhmed, KabiruHalilu, Abubakar Sani
18页
查看更多>>摘要：Conjugate gradient methods stand out as the most ideal iterative algorithms for solving nonlinear system of equations with large-dimensions. This is due to the fact that they are implemented with less memory and because of their ability to converge globally to solutions of problems considered. One of the most essential iterative method in this category is the Polak-Ribiere-Polyak (PRP) scheme, which is numerically effective, but its search directions are mostly not descent directions. In this paper, based upon the adaptive PRP scheme by Yuan et al. and the projection method, a numerically efficient PRP-type scheme for system of monotone nonlinear equations is presented, where the solution is restricted to a closed convex set. Apart from the ability to satisfy the condition that is quite vital for global convergence, a distinct novelty of the new scheme is its application in compressive sensing, where it is applied to restore blurry images. The scheme's global convergence is established with mild assumptions. Preliminary numerical results show that the method proposed is promising.(C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The C-0 stable generalized finite element methods (SGFEM) were recently developed for the elliptic source and eigenvalue problems with interfaces. This paper generalizes the SGFEM construction from its underlying C-0 finite element basis to isogeometric analysis (IGA) with Cp-1 B-spline basis. The main challenge is how to construct globally (except where at the interfaces) Cp-1 enriched functions while restraining the resulting condition number from faster growth. A technique based on transformations between the B splines and the Bernstein-Bezier polynomials is applied to meet the Cp-1 continuity requirement for enriched functions of arbitrary degree, and ensure good conditioning when the underlying IGA space is linear or quadratic. We establish the optimal error convergence of the approximate solutions for the elliptic source and eigenvalue problems with an interface for arbitrary degree. We verify our theoretical findings in various examples including both source and eigenvalue problems. We also make comparisons of the method with the SGFEM on computational time efficiency, scaled condition numbers(SCN), spectrum approximation and error convergences.(C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Based on derivatives of a Gaussian density, the Gram-Charlier series is an infinite expansion. Its truncated series is often used in many fields to approximate probability density functions. Although the expansions are useful, there are constrained regions on the value of the cumulants (or moments) that admit a valid (nonnegative) probability density function. When the truncation order is low (just at fourth-order), the truncated Gram- Charlier density may be difficult to approximate an implied probability distribution as closely as possible, especially for distributions that are not sufficiently close to a normal distribution. One might increase the order after which the series is truncated until a perfect fit is achieved. However, the series expansion is usually truncated in the existing literature until the fourth-order term because it becomes difficult to find valid regions. This paper shows how the valid region of higher cumulants can be numerically implemented by the semi-definite algorithm, which ensures that a series truncated at a cumulant of arbitrary even order represents a valid probability density. We provide examples of two valid regions of the sixth and eighth Gram-Charlier densities (i.e., truncated at the sixth and eighth terms). Our analysis proves the fact that valid regions can be broadened with the higher-order expansions. Furthermore, the impact of higher cumulants on the valid regions has been shown. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
Caboussat, AlexandreGourzoulidis, DimitriosPicasso, Marco
21页
查看更多>>摘要：Orthogonal maps are two-dimensional mappings that are solutions of the so-called origami problem obtained when folding a paper. These mappings are piecewise linear, and the discontinuities of their gradient form a singular set composed of straight lines representing the folding edges. The proposed algorithm relies on the minimization of a variational principle discussed in Caboussat et al. (2019). A splitting algorithm for the corresponding flow problem derived from the first-order optimality conditions alternates between local nonlinear problems and linear elliptic variational problems at each time step. Anisotropic adaptive techniques allow to obtain refined triangulations near the folding edges while keeping the number of vertices as low as possible. Numerical experiments validate the accuracy and efficiency of the adaptive method in various situations. Appropriate convergence properties are exhibited, and solutions with sharp edges are recovered. (C)& nbsp;2021 The Author(s). Published by Elsevier B.V.& nbsp;
查看更多>>摘要：In this paper, we study the valuation problem of life-contingent lookback options embedded in variable annuity with guaranteed minimum death benefit (GMDB). Specifically, the underlying asset price process is assumed to be an exponential regime-switching Levy process, which is observed periodically. The Fourier cosine series expansion method is applied to compute exponential moments of the discretely monitored maximum and minimum of the regime-switching Levy process. Furthermore, some explicit pricing formulas for the life-contingent lookback options embedded in GMDB products are derived. Finally, numerical experiments confirm the accuracy and efficiency of our method. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Eighty years ago J.C. Jaeger et al. introduced a class of improper integrals, currently called "Jaeger integrals " that occur in theoretical models of diverse physical phenomena characterized by cylindrical geometry. One application area is electroanalytical chemistry, where, in particular, the limiting Faradaic current in a potential step chronoamperometric experiment at a cylindrical electrode is described by the Jaeger J(0, 1; t) integral. In a recently published paper the first author determined the Laplace transform of the nonlimiting Faradaic current for a reversible charge transfer between members of a redox couple characterized by different diffusion coefficients. In this study we invert the novel Laplace transform and observe that, while it cannot be expressed by any of the Jaeger integrals, it can be perceived as a generalization of the J(0, 1; t) integral. We also describe how to compute this integral with the modulus of the relative error close to 10(-16) or smaller, using a C++ code employing exclusively standard floating point variables, without resorting to quad precision or other external high precision libraries. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This manuscript presents an extensive comparative analysis between a staggered and a monolithic solution technique for the bidomain equations of cardiac electrophysiology in the context of finite element method. For the monolithic solution technique, we adopt the work of Dal et al. (CMBBE 15: 645-656, 2012), where the parabolic and elliptic partial differential equations (PDEs) of the bidomain model are solved simultaneously and all rate equations are treated with an implicit time integration scheme. For the staggered scheme, however, we simply suggest a decoupled solution of the parabolic and elliptic PDE while keeping other aspects of the monolithic algorithm the same, such as utilization of the implicit time integration scheme, coupling of ordinary differential equations, which describe the state variables of cardiac electrophysiology, to the parabolic PDE and consideration of the transmembrane potential and the extracellular potential as degrees of freedom. Both solution algorithms are applied to several problems where we simulate regular planar wave propagations, scroll waves and externally applied electrical fields for different spatial and temporal resolution and material parameters. The comparison between the solution schemes is performed in terms of accuracy, efficiency and stability. We reveal that the suggested staggered solution scheme yields almost identical results with the monolithic scheme for physiological conductivity parameters and small time increments. Besides, the staggered scheme provides an enormous gain in computational efficiency, particularly, as the number of degrees of freedom is increased and we do not encounter any stability issue arising from the decoupled solution of the PDEs. Therefore, we conclude that the suggested fully implicit staggered solution algorithm has a tremendous application potential for the bidomain equations of cardiac electrophysiology. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
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