Search results for "Computational Mathematic"
showing 10 items of 987 documents
Regularization of optical flow with M-band wavelet transform
2003
The optical flow is an important tool for problems arising in the analysis of image sequences. Flow fields generated by various existing solving techniques are often noisy and partially incorrect, especially near occlusions or motion boundaries. Therefore, the additional information on the scene gained from a sequence of images is usually worse. In this paper, discrete wavelet transform has been adopted in order to enhance the reliability of optical flow estimation. A generalization of the well-known dyadic orthonormal wavelets to the case of the dilation scale factor M > 2 with N vanishing moments has been used, and it has proved to be a useful regularizing tool. The advantages in the comp…
A regular variational boundary model for free vibrations of magneto-electro-elastic structures
2011
In this paper a regular variational boundary element formulation for dynamic analysis of two-dimensional magneto-electro-elastic domains is presented. The method is based on a hybrid variational principle expressed in terms of generalized magneto-electro-elastic variables. The domain variables are approximated by using a superposition of weighted regular fundamental solutions of the static magneto-electro-elastic problem, whereas the boundary variables are expressed in terms of nodal values. The variational principle coupled with the proposed discretization scheme leads to the calculation of frequency-independent and symmetric generalized stiffness and mass matrices. The generalized stiffne…
Initial strain effects in multilayer composite laminates
2001
A boundary integral formulation for the analysis of stress fields induced in composite laminates by initial strains, such as may be due to temperature changes and moisture absorption is presented. The study is formulated on the basis of the theory of generalized orthotropic thermo-elasticity and the governing integral equations are directly deduced through the generalized reciprocity theorem. A suitable expression of the problem fundamental solutions is given for use in computations. The resulting linear system of algebraic equations is obtained by the boundary element method and stress interlaminar distributions in the boundary-layer are calculated by using a boundary only discretization. …
BIEM-based variational principles for elastoplasticity with unilateral contact boundary conditions
1998
The structural step problem for elastic-plastic internal-variable materials is addressed in the presence of frictionless unilateral contact conditions. Basing on the BIEM (boundary integral equation method) and making use of deformation-theory plasticity (through the backward-difference method of computational plasticity), two variational principles are shown to characterize the solution to the step problem: one is a stationarity principle having as unknowns all the problem variables, the other is a saddle-point principle having as unknowns the increments of the boundary tractions and displacements, along with the plastic strain increments in the domain. The discretization by boundary and i…
Controllability method for acoustic scattering with spectral elements
2007
We formulate the Helmholtz equation as an exact controllability problem for the time-dependent wave equation. The problem is then discretized in time domain with central finite difference scheme and in space domain with spectral elements. This approach leads to high accuracy in spatial discretization. Moreover, the spectral element method results in diagonal mass matrices, which makes the time integration of the wave equation highly efficient. After discretization, the exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. We illustrate the method with some numerical experiments, which demonstrate the significant improveme…
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
2021
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide r…
ADI schemes for valuing European options under the Bates model
2018
Abstract This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.
A wavelet-based tool for studying non-periodicity
2010
This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is based on the continuous wavelet transform and the wavelet multiresolution analysis. A new parameter, the \textit{scale index}, is introduced and interpreted as a measure of the degree of the signal's non-periodicity. This methodology is successfully applied to three classical dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and the Henon map.
Optimal Control Under Fuzzy Conditions for Dynamical Systems Associated with the Second Order Linear Differential Equations
2020
This paper is devoted to an optimal trajectory planning problem with uncertainty in location conditions considered as a problem of constrained optimal control for dynamical systems. Fuzzy numbers are used to incorporate uncertainty of constraints into the classical setting of the problem under consideration. The proposed approach applied to dynamical systems associated with the second order linear differential equations allows to find an optimal control law at each \(\alpha \)-level using spline-based methods developed in the framework of the theory of splines in convex sets. The solution technique is illustrated by numerical examples.
Detecting tri‐stability of 3D models with complex attractors via meshfree reconstruction of invariant manifolds of saddle points
2018
In mathematical modeling it is often required the analysis of the vector field topology in order to predict the evolution of the variables involved. When a dynamical system is multi-stable the trajectories approach different stable states, depending on the initialmconditions. The aim of this work is the detection of the invariant manifolds of thesaddle points to analyze the boundaries of the basins of attraction. Once that a sufficient number of separatrix points is found a Moving Least Squares meshfree method is involved to reconstruct the separatrix manifolds. Numerical results are presented to assess the method referring to tri-stable models with complex attractors such as limit cycles o…