Browsing by Author "Hakula, Harri"

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  • Adaptive reference elements via harmonic extensions and associated inner modes
    (2020-12-01) Hakula, Harri
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    A non-intrusive extension to the standard p-version of the finite element method is proposed. Meshes with hanging nodes are handled by adapting the reference elements so that the resulting discretisation is always conforming. The shape functions on these adaptive reference elements are not polynomials, but either harmonic extensions of the boundary restrictions of the standard shape functions or solutions to a local Poisson problem. The numerical experiments are taken from computational function theory and the efficiency of the proposed extension resulting in exponential convergence in the quantities of interest is demonstrated.
  • Anturirunkojen lämpödeformaation kolmiulotteinen analyysi
    (1991) Hakula, Harri
     Helsinki University of Technology | Master's thesis
  • Assessing the Structural Performance of Biodegradable Capsules
    (2023-08-14) Hakula, Harri
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Biodegradable materials pose challenges over all aspects of computational mechanics. In this study, the focus is on the resulting domain uncertainty. Model structures or devices are shells of revolution subject to random variation of the outer surface. The novelty of the proposed computational approach is the possibility to restrict the variation to specific parts of the structure using a posteriori filtering, which is applied to the random process whose realisations are the profiles of the shells. The dimensionally reduced stochastic elasticity problems are solved using a collocation method where every realisation is discretised separately. The collocation scheme is validated against standard Monte Carlo. The reliability of the simulations is further confirmed via a posteriori error estimates that are computed using the same collocation scheme. The quantities of interest on the nominal domain are the expected displacement fields and their variances.
  • Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems
    (2019-01-01) Hakula, Harri; Laaksonen, Mikael
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite dimensional space formed as the tensor product of the approximation space for the underlying stochastic function space, and the approximation space for the underlying spatial function space. Sparse polynomial approximation is employed to obtain the first one, while classical finite elements are employed to obtain the latter. An error analysis is presented for the asymptotic convergence of the spectral inverse iteration to the smallest eigenvalue and the associated eigenvector of the problem. A series of detailed numerical experiments supports the conclusions of this analysis.
  • Automatic detection of mistakes in a computerised tower task
    (2022-02-25) Lymysalo, Venla
     Perustieteiden korkeakoulu | Bachelor's thesis
  • Chemometric calibration for Raman spectral analysis - Machine learning and hard modeling in CHO cell culture applications
    (2023-12-12) Lane, Sofia
     Perustieteiden korkeakoulu | Master's thesis
    In this thesis, support vector regression (SVR), science-based calibration (SBC), and partial least square (PLS) regression models are constructed for lactate, ammonia, and amino acid concentration in Chinese hamster ovary (CHO) cell cultures. To construct and test said models, data from five different CHO perfusion bioreactor runs was obtained, consisting of time-gated Raman spectra and the concentrations of the analytes of interest that coincide with the given spectra. In addition to the data from the bioreactor runs, response spectra of the various amino acids and of the bioreactor media were obtained for conducting SBC. It was found that both SVR and PLS models produce predictions of satisfactory accuracy for roughly half of the analytes, with the best results occurring for amino acids. When comparing the results of the SVR and PLS models, we saw that in nearly every case, SVR can produce more accurate predictions than PLS, especially when non-linear forms of SVR are utilized. When it comes to SBC, we were unable to produce models with adequate accuracy, due to a failure to accurately scale the response spectra of the various analytes to represent the change in intensity per unit concentration. As far as the need for reference data, although the results were not satisfactory, the processes involved with SBC required a fraction of the reference data that PLS and SVR did.
  • Collocation method for solving stochastic elasticity problems with an uncertain domain
    (2015-02-24) Lehtonen, Jonatan
     Perustieteiden korkeakoulu | Master's thesis
    In this thesis, we formulate a method for determining how quantities such as stress in an elastic body change depending on its shape. This stochastic elasticity problem has important applications in structural analysis and design, such as determining how manufacturing flaws affect the properties of an object. We assume that the shape of the object depends on some stochastic parameters, and use a combination of multivariate interpolation and conformal mappings to solve the problem. The interpolation allows us to reduce the stochastic problem to a collection of deterministic elasticity problems, which are solved by using existing finite element analysis software, and the conformal mappings are used to accommodate the varying shape of the object. A sparse grid interpolation scheme is used to diminish the curse of dimensionality related to multivariate interpolation. We define model problems involving two stochastic parameters, for both 2D and 3D objects. The implementation of the method is described in detail, and numerical results are provided for the model problems. With as few as 29 deterministic problems, we reach the point where the interpolation accuracy cannot be improved due to the inherent inaccuracy of the finite element solutions.
  • Termokemiallisen tasapainon laskemisesta
    (2010) Baarman, Lars
     School of Science | Master's thesis
    The objective of this thesis is to present a new optimization algorithm for calculating the thermo chemical balance in Outotec's HSC-Chemistry -software. The thesis includes the presentation; further development and implementation, as well as testing of an interior point method. The results of the algorithm are compared to the ones of the earlier algorithm, and the suitability of the method is evaluated. The aim is to acquire a more robust optimization method, as the earlier algorithm is not reliable enough. The thermo chemical potential is obtained by minimizing Gibbs energy. The optimization method is a primal-dual interior point method that is further developed to fit the problem at hand. The new method is tested on 1901 problems that are found in 38 files given by Outotec. In the testing all the given optimization problems are solved, when the preceding method is unable to solve almost 300 of the same problems. In addition it is noticed that there are a huge number of problems to which both methods give a solution, although they differ substantiality. In all of these cases the new developed method offers the better solution. The applicability of the developed algorithm is evaluated and in conclusions the developed algorithm is better and it is recommended to implement it into the commercial software. There are however a few proposals of further development and suggestions about the incorporation into the HSC-Chemistry -module.
  • Conformal capacity and polycircular domains
    (2023-03-01) Hakula, Harri; Nasser, Mohamed M.S.; Vuorinen, Matti
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by polycircular domains. Experimental error estimates are provided for the computed capacity and, when possible, the rate of convergence under refinement of discretization is analyzed. The main ingredients of the computation are two computational methods, on one hand the boundary integral equation method combined with the fast multipole method and on the other hand the hp-FEM method. The results obtained with these two methods agree with high accuracy.
  • Conformal moduli of symmetric circular quadrilaterals with cusps
    (2021) Hakula, Harri; Nasyrov, Semen; Vuorinen, Matti
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    We investigate moduli of planar circular quadrilaterals that are symmetric with respect to both coordinate axes. First we develop an analytic approach that reduces this problem to ODEs and then devise a numerical method to find out the accessory parameters. This method uses the Schwarz equation to determine a conformal mapping of the unit disk onto a given circular quadrilateral. We also give an example of a circular quadrilateral for which the value of the conformal modulus can be found in analytic form. This example is used to validate the numeric calculations. We also apply another method, the so called hpFEM, for the numerical calculation of the moduli. These two different approaches provide results agreeing with high accuracy.
  • Conformal modulus and planar domains with strong singularities and cusps
    (2018-01-01) Hakula, Harri; Rasila, Antti; Vuorinen, Matti
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    We study the problem of computing the conformal modulus of rings and quadrilaterals with strong singularities and cusps at their boundary. We reduce this problem to the numerical solution of the associated Dirichlet and Dirichlet-Neumann-type boundary values problems for the Laplace equation. Several experimental results, with error estimates, are reported. In particular, we consider domains with dendrite-like boundaries where an analytic formula for the conformal modulus can be derived. The boundary value problems are solved using an hp-finite element method.
  • The Conjugate Function Method and Conformal Mappings in Multiply Connected Domains
    (2019) Hakula, Harri; Quach, Tri; Rasila, Antti
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method is generalized for multiply connected domains. The key challenge addressed here is the construction of the conjugate domain and the associated conjugate problem. All variants of the method preserve the so-called reciprocal relation of the moduli. An implementation of the algorithm is given along with several examples and illustrations.
  • Conjugate function method for numerical conformal mappings
    (2011) Hakula, Harri; Quach, Tri; Rasila, Antti
     Perustieteiden korkeakoulu | D4 Julkaistu kehittämis- tai tutkimusraportti tai -selvitys
  • Cylindrical Shell with Junctions: Uncertainty Quantification of Free Vibration and Frequency Response Analysis
    (2018-12-02) Laaksonen, Mikael; Hakula, Harri; Kaarnioja, Vesa
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Numerical simulation of thin solids remains one of the challenges in computational mechanics. The 3D elasticity problems of shells of revolution are dimensionally reduced in different ways depending on the symmetries of the configurations resulting in corresponding 2D models. In this paper, we solve the multiparametric free vibration of complex shell configurations under uncertainty using stochastic collocation with the p-version of finite element method and apply the collocation approach to frequency response analysis. In numerical examples, the sources of uncertainty are related to material parameters and geometry representing manufacturing imperfections. All stochastic collocation results have been verified with Monte Carlo methods.
  • Effects of Internal Boundary Layers and Sensitivity on Frequency Response of Shells of Revolution
    (2023-09) Hakula, Harri
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    New applications introduced capsule designs with features that have not been fully analysed in the literature. In this study, thin shells of revolution are used to model drug delivery capsules both with closed and open designs including perforations. The effects of internal boundary layers and sensitivity on frequency response are discussed in the special case with symmetric concentrated load. The simulations are carried out using high-order finite element method and the frequency response is computed with a very accurate low-rank approximation. Due to the propagation of the singularities induced by the concentrated loads, the most energetic responses do not necessarily include a pinch-through at the point of action. In sensitive configurations, the presence of regions with elliptic curvature leads to strong oscillations at lower frequencies. The amplitudes of these oscillations decay as the frequencies increase. For efficient and reliable analysis of such structures, it is necessary to understand the intricate interplay of loading types and geometry, including the effects of the chosen shell models.
  • Efficient finite element method to estimate eddy current loss due to random interlaminar contacts in electrical sheets
    (2018) Shah, Sahas Bikram; Rasilo, Paavo; Hakula, Harri; Arkkio, Antero
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Electrical sheets of electrical machines are laminated to reduce eddy current loss. However, a series of punching and pressing processes form random galvanic contacts at the edges of the sheets. These galvanic contacts are random in nature and cause an additional eddy current loss in the laminated cores. In this paper, a stochastic Galerkin finite element method is implemented to consider random interlaminar contacts in the magnetic vector potential formulation. The random interlaminar conductivities at the edges of the electrical sheets are approximated using a conductivity field and propagated through the finite element formulation. The spatial random variation of the conductivity causes the solution to be random, and hence, it is approximated by using a polynomial chaos expansion method. Finally, the additional eddy current losses due to the interlaminar contacts are estimated from a stochastic Galerkin method and compared with a Monte Carlo method. Accuracy and computation time of both models are discussed in the paper.
  • Eräs hp-adaptiivinen elementtimenetelmä kuoriyhtälöille
    (2010) Tuominen, Tomi
     School of Science | Licentiate thesis
    In this work solving of shell equations by an hp-adaptive finite element method (FEM) is studied. Shells are thin objects of curved mid-surface. Thickness of a shell is assumed to be notably smaller than its other dimensions, for example the diameter of the object. Mathematically shells can be considered as two-dimensional objects, and in dimension reduced models equations are written on the mid-surface of the object. Solution of the shell equations contains various boundary and internal layer components in addition to global length scales. Locking and large condition number of a system can cause problems as well, when equations are solved numerically. Shell equation are solved numerically by FEM. Accuracy of a solution is improved in stages by an adaptive method, in which it is possible to refine the mesh and raise or lower the degree of an element. In addition to usual error indicator, an hp-indicator is required to decide whether an element is split or polynomial degree is changed. In this work the smoothness of the solution is estimated by a method based on the Sobolev-regularity of a function. The smoother the solution is the higher degree of polynomial can be used. In dimension reduced models the elastic energy of the shell consists mainly of bending and membrane energy. In some shell models like Reissner-Naghdi, which is in use here, also shear energy is involved. However its contribution to the total energy is usually very small. Especially bending dominated cases include a risk of numerical locking. Locking appears when discrete variation space is too small and best approximate solution is just too far from the accurate solution. The best way to prevent locking is to use sufficient high order elements globally. In this work also a method to detect the risk of locking is studied. In that method the problem is solved by minimal amount of elements and different polynomial degrees. This way it is quite reliable to decide whether the problem is bending or membrane dominated. In numerical experiments the hp-adaptive FEM works quite well in sense of deciding element and polynomial degree distributions. In the areas of different layers, the degree of polynomial is not raised too much until the mesh is dense enough. Problems due to locking and large condition number appear clearly in bending dominated case. In calculations locking prevention schemes, such as setting a lower bound for polynomial degree, have not been used.
  • Feature Extraction of Multispectral Mobile Laser Scanner Data
    (2019-06-10) Savela, Joona
     Perustieteiden korkeakoulu | Bachelor's thesis
  • Finite Element Methods for Stochastic Eigenvalue Problems
    (2014) Laaksonen, Mikael
     Perustieteiden korkeakoulu | Master's thesis
    In this thesis we consider finite element methods for stochastic eigenvalue problems. As a model problem we will consider the eigenvalue problem of an elliptic diffusion operator, where the diffusion coefficient is assumed to be a random field. We discuss the fundamental theory of discretizing equations of this kind and consider methods of approximately solving them. We present two numerical schemes of solving the model problem. The first one is a specific combination of the stochastic Galerkin method, stochastic collocation method, and the Rayleigh quotient iteration. The second approach is a pure collocation method, where we use Smolyak sparse grids to reduce the number of collocation points. We illustrate the convergence and functionality of the presented methods by applying them to the model problem. The stochastic collocation method is found to be a reliable choice. The Rayleigh quotient iteration scheme also seems to have potential, although it significantly overestimates the variance of the solution.
  • Free vibration of perforated cylindrical shells of revolution: Asymptotics and effective material parameters
    (2023-01-01) Giani, Stefano; Hakula, Harri
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Free vibration characteristics of thin perforated shells of revolution vary depending not only on the dimensionless thickness of the shell but also on the perforation structure. For any given configuration there exists a critical value of the dimensionless thickness below which homogenisation fails. The failure occurs when the modes do not have corresponding counterparts in the non-perforated reference shell. Within the admissible range of thicknesses the uniform effective material parameters are derived with a minimisation process. During the process every observed mode is matched with a corresponding reference one using a problem-specific characterisation. The performance of the derived effective material parameters and hence the minimisation process is demonstrated with an extensive set of numerical experiments. Limitations of the proposed approach are reflected in relation to idealised trommel screen configurations.