Browsing by Author "Parviainen, Mikko"

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  • Global higher integrability for nonlinear parabolic partial differential equations in nonsmooth domains
    (2007-11-02) Parviainen, Mikko
     Doctoral dissertation (monograph)
    This thesis studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates near the lateral and initial boundaries. The results of the thesis extend to parabolic systems as well. The higher integrability estimates provide a useful tool in several applications.
  • Global higher integrability for nonlinear parabolic problems in nonsmooth domains
    (2005) Parviainen, Mikko
     Helsinki University of Technology | Licentiate thesis
  • Implementation of Industrial Internet to discrete automation devices
    (2016-12-12) Parviainen, Mikko
     Insinööritieteiden korkeakoulu | Master's thesis
    Industrial Internet is a term that is used to describe digitalization of industry. It is a research direction in Finland, where there are already various groups studying it. Despite this, the term Industrial Internet is still relatively vague and there is a lack of concreteness around the topic. The objective of this thesis is to explore the current status of Industrial Internet and study the capabilities of automation devices from an Industrial Internet point of view. I explore Industrial Internet through a literary review where I study various use cases. The use cases of Industrial Internet are divided into two main types: platform centric and machine to machine (M2M) communication centric. The use cases provide a list of characteristics and requirements for Industrial Internet from these two perspectives. General requirements are, for example scalability and flexibility, which are achieved through various IT technologies, such as Service-Oriented-Architecture. This thesis also consists of a practical part where I configured the control logic and data collection for a test bed that simulates drop tests of active magnetic bearings. The control logic consists of a programmable logic controller and corresponding software. The data collection consists of software for collecting and analyzing measurement data and the measuring equipment. After the literary review and practical part, I propose the creation of a cloud based Industrial Internet platform around the active magnetic test bed. The purpose of the platform is to provide a direction for further research. The creation of the platform consists of two phases: first phase includes the creation of the platform so that the test bed achieves current functionality but cloud based. The second phase consists of changing the platform to meet the requirements of the literature review. The end results will be an application independent system solution for Industrial Internet.
  • Satunnaiskävelyn yhteys harmonisiin funktioihin
    (2010) Lindfors, Casimir
     Informaatio- ja luonnontieteiden tiedekunta | Bachelor's thesis
  • Systemaattisten ideointimenetelmien käyttö ja hyödyt tuotekehityksessä
    (2013-12-13) Parviainen, Mikko
     Insinööritieteiden korkeakoulu | Bachelor's thesis
  • Wavelet methods for conservation laws
    (2003) Parviainen, Mikko
     Helsinki University of Technology | Master's thesis
    In this thesis hyperbolic partial differential equations arising from conservation laws are studied both numerically and analytically. The differential equations are of the form u(x, t)t + f(u{x, t))x = 0, where u is a function to be solved and f is a smooth possibly nonlinear function. For example, solving a gas flow when mass is conserved leads to the partial differential equations of this type. Due to nonlinearity the conservation law may not have a classical solution, and therefore weak solutions are formulated. To guarantee the uniqueness of the weak solutions additional entropy conditions, like Kruzkov's entropy condition, are needed. We prove the uniqueness of the solution satisfying Kruzkov's entropy condition and formulate the existence result. The formulation of the uniqueness result differs from the usual formulation given in the literature. In the numerical part, we study the discontinuous Galerkin methods, like for example Godunov's scheme, which is the simplest of such methods. To guarantee the convergence of the numerical method to the right solution, some extra conditions must be required. The Lax-Wendroff theorem, which states when the obtained numerical solution is the right one, is proved with more general conditions than in [26]. Also stability results are considered. Wavelets and scaling functions obtained from the orthonormal multiresolution can be applied to the discontinuous Galerkin method. Then the numerical solution can be efficiently divided into high and low frequency parts. By controlling the high frequency part, we can develop adaptive methods and aim the computational power to the right places. In addition, pyramid algorithms can be used to obtain different refinement levels of the numerical solution efficiently. Especially multiwavelets seem to be attractive for the numerical solvers due to their simplicity. At the end of the thesis, we suggest a high order generalization for the known low order adaptive wavelet method. Also a new possibility for damping spurious oscillations in high order solutions is suggested. Numerical experiments are performed for the introduced methods in the case of Burgers' equation ut + uux = 0. The reader is expected to have basic knowledge of real analysis and of the theory of partial differential equations. The presentation is mainly self-contained.