Search results for "numeeriset menetelmät"

Electromagnetic wave propagation in non-homogeneous waveguides

2015

We investigate an electromagnetic waveguide, having several cylindrical ends. The waveguide is assumed to be empty and to have a perfectly conductive boundary. We study the electromagnetic field, excited in the waveguide in the presence of charges and currents. The field can be described as a solution of the stationary Maxwell system with conductive boundary conditions and “intrinsic” radiation conditions at infinity. We prove the problem to be well-posed. Electromagnetic waves propagation in the waveguide can be described by means of a scattering matrix. We introduce such a matrix for all values of the spectral parameter k in the waveguide continuous spectrum and study its properties. Moreove…

Convergence of dynamic programming principles for the $p$-Laplacian

2018

We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

A fast Fourier transform based direct solver for the Helmholtz problem

2018

This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is O(N log N) operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed…

Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research

2022

Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple and Wolfram Alpha, the location of the largest and the smallest roots responsible for the cycles of period p among the roots responsible for the cycles of periods 2kp (period-doubling) and kp (period-multiplying) has been determined. These purely computational results of experimental mathematics, made possible by the use of modern digital tools, can be used as a motivation for confirmation through not-yet-developed methods of formal mathematics. peerReviewed

Analysis of oscillations in discontinuous Lurie systems via LPRS method

2019

We discuss advantages and limitations of the harmonic balance method and the locus of a perturbed relay system (LPRS) method in the problem of finding periodic oscillations. In this paper we present the results of using harmonic balance method and LPRS method while investigating a 3rd order dynamic system in Lurie form. In this system a symmetric periodic oscillation is found, while other two asymmetric periodic motions are not found using both methods. peerReviewed

On superconvergence techniques

1984

Modeling of intracellular transport in realistic cell geometries

2018

The transport of molecules inside cells is a complex process, the characterization of which is important to gain full understanding of cellular processes. Understanding of intracellular transport is also important for medical applications, for example when analyzing transport of medicine inside cells. The intracellular environment is very complex, and at least the most crucial parts of this complexity must be accounted for to solve transport problems in cells. In this thesis the results of studies in modeling intracellular transport are presented. The aim of the work was to model intracellular transport of proteins and viral capsids in realistic cell environments. To this end, microscopic m…

Numeeriset yhtälönratkaisumenetelmät

2017

Tämän tutkielman tavoitteena on käsitellä numeerisia yhtälönratkaisumenetelmiä matematiikan aineenopettajan näkökulmasta ja toimia lukion numeerisen matematiikan kurssin opettajan taustamateriaalina. Keskeinen sisältö käsittelee Lipschitz-jatkuvuutta, iteraatiota sekä Newton-Raphsonin menetelmää. Yhtälönratkaisu ja kahden lausekkeen yhtäsuuruuksien vertailu palautuu aina matematiikan klassiseen ongelmaan funktion nollakohdan etsimisestä. Keskeiset numeerisen yhtälönratkaisun metodit ovat rekursio ja iteraatio. Rekursio tarkoittaa oleellisesti toistoa. Iteraatiossa edellinen likiratkaisu ohjaa tarkentavasti seuraavan likiratkaisun laskentaa. Tällöin muodostuu tarkentuvien likiratkaisuiden lu…

Spectral analysis and quantum chaos in two-dimensional nanostructures

2015

This thesis describes a study into the eigenvalues and eigenstates of twodimensional (2D) quantum systems. The research is summarized in four scientific publications by the author. The underlying motivation for this work is the grand question of quantum chaos: how does chaos, as known in classical mechanics, manifest in quantum mechanics? The search and analysis of these quantum fingerprints of chaos requires efficient numerical tools and methods, the development of which is given a special emphasis in this thesis. The first publication in this thesis concerns the eigenspectrum analysis of a nanoscale device. It is shown that a measured addition energy spectrum can be explained by a simple …

An approach to linguistic pattern recognition using fuzzy systems

2003

Jouni Raitamäen väitöskirjan tarkoituksena on löytää menetelmiä sumeiden kielellisten JOS-NIIN -tyypisten sääntöjen tuottamiseen numeerisesta tiedosta. Apuna tässä käytetään sumeiden järjestelmien teoriaa.Menetelmien antamien tulosten tulee olla sekä ymmärrettäviä että tarkkoja. Kuitenkin vaatimus on yleensä ristiriitainen, sillä riittävän tarkan ratkaisun saavuttaminen vaatii usein monimutkaisempia menetelmiä ja malleja. Tämä ymmärrettävyyden ja tarkkuuden välinen tasapaino sumeissa järjestelmissä on keskeisellä sijalla väitöskirjan tarkasteluissa.Raitamäen tavoitteena on löytää sumea järjestelmä, joka on riittävän yleinen siten, että sitä voi soveltaa pienin modifikaatioin sekä regressio-…