Search results for "Poisson Equation"

Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation

2018

The paper deals with the generalization of Fourier-type relations in the context of fractional-order calculus. The instantaneous temperature-flux equation of the Fourier-type diffusion is generalized, introducing a self-similar, fractal-type mass clustering at the micro scale. In this setting, the resulting conduction equation at the macro scale yields a Caputo's fractional derivative with order [0,1] of temperature gradient that generalizes the Fourier conduction equation. The order of the fractional-derivative has been related to the fractal assembly of the microstructure and some preliminary observations about the thermodynamical restrictions of the coefficients and the state functions r…

On FE-grid relocation in solving unilateral boundary value problems by FEM

1992

We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions, Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction. peerReviewed

SPH modeling of blood flow in cerebral aneurysms

Gli aneurismi cerebrali sono dilatazioni patologiche di arterie cerebrali. Queste patologie hanno un intrinseco rischio di rottura con conseguenti emorragie intracraniche. Sebbene i meccanismi di formazione, crescita e rottura degli aneurismi cerebrali non sono ancora del tutto compresi, è comunemente riconosciuto che in questi processi i fattori emodinamici giocano un ruolo molto importante. Le simulazioni numeriche possono fornire utili informazioni sull'emodinamica e possono essere usate per applicazioni cliniche. Nei tradizionali metodi numerici basati su una griglia di calcolo il processo di discretizzazione dei vasi cerebrali sui quali insiste un aneurisma è molto complesso. D’altra p…

Poissonin yhtälön nopeat ratkaisijat

2016

Tutkielmassa esitellään Poissonin yhtälö sekä sen diskretointi. Lisäksi käydään läpi kaksi nopeaa numeerista menetelmää yhtälön ratkaisemiseksi. Yksinkertaisuuden vuoksi rajoitutaan kaksiulotteisiin tehtäviin, joissa on voimassa Dirichle’t reunaehto. Ensimmäinen menetelmistä on monihilamenetelmä, joka on iteratiivinen menetelmä, ja toisena syklinen reduktio, joka on suora menetelmä. Molemmat menetelmät ovat hyvin tehokkaita sekä helposti rinnakkaistuvia. In this thesis we introduce Poisson’s equation and its discretization. In addition we go through two fast numerical methods for solving the equation. The thesis is limited only to two-dimensional cases with Dirichlet boundary condition. The…

The Homogeneous Poisson Point Process

2008