### Browsing by Author "Laaksonen, Mikael"

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Item Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems(SPRINGER HEIDELBERG, 2019-01-01) Hakula, Harri; Laaksonen, Mikael; Department of Mathematics and Systems Analysis; Numerical AnalysisWe 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.Item Comparison of auxiliary power production methods in a controllable pitch propeller vessel with shaft generators(2021-05-10) Koski, Kim; Laaksonen, Mikael; Sähkötekniikan korkeakoulu; Turunen, MarkusItem Cylindrical Shell with Junctions: Uncertainty Quantification of Free Vibration and Frequency Response Analysis(2018-12-02) Laaksonen, Mikael; Hakula, Harri; Kaarnioja, Vesa; Department of Mathematics and Systems AnalysisNumerical 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.Item Effect of xenon on brain injury, neurological outcome, and survival in patients after aneurysmal subarachnoid hemorrhage—study protocol for a randomized clinical trial(BioMed Central, 2023-12) Laaksonen, Mikael; Rinne, Jaakko; Rahi, Melissa; Posti, Jussi P.; Laitio, Ruut; Kivelev, Juri; Saarenpää, Ilkka; Laukka, Dan; Frösen, Juhana; Ronkainen, Antti; Bendel, Stepani; Långsjö, Jaakko; Ala-Peijari, Marika; Saunavaara, Jani; Parkkola, Riitta; Nyman, Mikko; Martikainen, Ilkka K.; Dickens, Alex M.; Rinne, Juha; Valtonen, Mika; Saari, Teijo I.; Koivisto, Timo; Bendel, Paula; Roine, Timo; Saraste, Antti; Vahlberg, Tero; Tanttari, Juha; Laitio, Timo; Department of Neuroscience and Biomedical Engineering; Turku University Hospital; Tampere University; University of Eastern Finland; University of Turku; Elomatic IndiaBackground: Aneurysmal subarachnoid hemorrhage (aSAH) is a neurological emergency, affecting a younger population than individuals experiencing an ischemic stroke; aSAH is associated with a high risk of mortality and permanent disability. The noble gas xenon has been shown to possess neuroprotective properties as demonstrated in numerous preclinical animal studies. In addition, a recent study demonstrated that xenon could attenuate a white matter injury after out-of-hospital cardiac arrest. Methods: The study is a prospective, multicenter phase II clinical drug trial. The study design is a single-blind, prospective superiority randomized two-armed parallel follow-up study. The primary objective of the study is to explore the potential neuroprotective effects of inhaled xenon, when administered within 6 h after the onset of symptoms of aSAH. The primary endpoint is the extent of the global white matter injury assessed with magnetic resonance diffusion tensor imaging of the brain. Discussion: Despite improvements in medical technology and advancements in medical science, aSAH mortality and disability rates have remained nearly unchanged for the past 10 years. Therefore, new neuroprotective strategies to attenuate the early and delayed brain injuries after aSAH are needed to reduce morbidity and mortality. Trial registration: ClinicalTrials.gov NCT04696523. Registered on 6 January 2021. EudraCT, EudraCT Number: 2019-001542-17. Registered on 8 July 2020.Item Finite Element Methods for Stochastic Eigenvalue Problems(2014) Laaksonen, Mikael; Hakula, Harri; Perustieteiden korkeakoulu; Perustieteiden korkeakoulu; Stenberg, RolfIn 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.Item Frequency response analysis of perforated shells with uncertain materials and damage(Springer International Publishing AG, 2019-12-01) Hakula, Harri; Laaksonen, Mikael; Department of Mathematics and Systems Analysis; LUT UniversityIn this paper, we give an overview of the issues one must consider when designing methods for vibration based health monitoring systems for perforated thin shells especially in relation to frequency response analysis. In particular, we allow either the material parameters or the structure or both to be random. The numerical experiments are computed using the standard high order finite element method with stochastic collocation for the cases with random material and Monte Carlo for those with damaged or random structures. The results display a wide range of responses over the experimental configurations. In perforated shell structures, the internal boundary layers can play an important role especially when damage is allowed within the penetration patterns. The computational methodology advocated here can be used to build statistical databases that are necessary for development of probabilistic damage identification methods.Item Hybrid Stochastic Finite Element Method for Mechanical Vibration Problems(IOS PRESS, 2015) Hakula, Harri; Laaksonen, Mikael; Department of Mathematics and Systems AnalysisItem Low-Rank Approximation of Frequency Response Analysis of Perforated Cylinders under Uncertainty(MDPI AG, 2022-04-01) Hakula, Harri; Laaksonen, Mikael; Department of Mathematics and Systems Analysis; Wartsila Corporation; Department of Mathematics and Systems AnalysisFrequency response analysis under uncertainty is computationally expensive. Low-rank approximation techniques can significantly reduce the solution times. Thin perforated cylinders, as with all shells, have specific features affecting the approximation error. There exists a rich thicknessdependent boundary layer structure, leading to local features becoming dominant as the thickness tends to zero. Related to boundary layers, there is also a connection between eigenmodes and the perforation patterns. The Krylov subspace approach for proportionally damped systems with uncertain Young’s modulus is compared with the full system, and via numerical experiments, it is shown that the relative accuracy of the low-rank approximation of perforated shells measured in energy depends on the dimensionless thickness. In the context of frequency response analysis, it then becomes possible that, at some critical thicknesses, the most energetic response within the observed frequency range is not identified correctly. The reference structure used in the experiments is a trommel screen with a non-regular perforation pattern with two different perforation zones. The low-rank approximation scheme is shown to be feasible in computational asymptotic analysis of trommel designs when the proportional damping model is used.Item Matkapuhelimen pudotuksen visualisointi(2012-09-27) Laaksonen, Mikael; Stenberg, Rolf; Turkkila, Timo; Perustieteiden korkeakoulu; Stenberg, RolfItem Multiparametric shell eigenvalue problems(Elsevier, 2019-01-01) Laaksonen, Mikael; Hakula, Harri; Department of Mathematics and Systems AnalysisThe eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs depend on a deterministic parameter, the dimensionless thickness. The stochastic subspace iteration algorithms presented here are capable of resolving the smallest eigenclusters. In the case of random material parameters, it is possible that the eigenmodes cross in the stochastic parameter space. This interesting phenomenon is demonstrated via numerical experiments. Finally, the effect of the chosen material model on the asymptotics in relation to the deterministic parameter is shown to be negligible.Item On Numerical Solution of Multiparametric Eigenvalue Problems(Aalto University, 2018) Laaksonen, Mikael; Hakula, Harri, Dr., Aalto University, Department of Mathematics and Systems Analysis, Finland; Matematiikan ja systeemianalyysin laitos; Department of Mathematics and Systems Analysis; Perustieteiden korkeakoulu; School of Science; Hyvönen, Nuutti, Prof., Aalto University, Department of Mathematics and Systems Analysis, FinlandIn this thesis, numerical methods for solving multiparametric eigenvalue problems, i.e., eigenvalue problems of operators that depend on a countable number of parameters, are considered. Such problems arise, for instance, in engineering applications, where a single deterministic problem may depend on a number of design parameters, or through parametrization of random inputs in physical systems with data uncertainty. The focus in this work is on approaches based on the stochastic Galerkin finite element method. In particular, we suggest a novel and efficient algorithm, the spectral inverse iteration, for computing approximate eigenpairs in the case of simple eigenvalues. This algorithm is also extended to a spectral subspace iteration, which allows computation of approximate invariant subspaces associated to eigenvalues of higher multiplicity. A step-by-step analysis is presented on the asymptotic convergence of the spectral inverse iteration and the results of this analysis are verified by a series of detailed numerical experiments. Convergence of the spectral subspace iteration is also illustrated in the numerical experiments, specifically for problems with eigenvalue crossings within the parameter space. Sparse stochastic collocation algorithms are used as reference when validating the output of the two algorithms. As an application of our algorithms we consider solving mechanical vibration problems with uncertain inputs. A hybrid method is suggested for computing eigenmodes of structures with randomness in both geometry and the elastic modulus. Furthermore, two different strategies are presented for computing the eigenmodes for a shell of revolution: one based on dimension reduction and separation of the eigenmodes by wavenumber, and another based on applying the algorithm of spectral subspace iteration directly to the original problem.Item Process improvements for transport aircraft redelivery(2017-10-30) Laaksonen, Mikael; Kanerva, Mikko; Ojala, Juha; Insinööritieteiden korkeakoulu; Kujala, PenttiItem Subspace reduction for stochastic planar elasticity(MDPI AG, 2022) Hakula, Harri; Laaksonen, Mikael; Department of Mathematics and Systems Analysis; Wärtsilä Finland; Department of Mathematics and Systems AnalysisStochastic eigenvalue problems are nonlinear and multiparametric. They require their own solution methods and remain one of the challenge problems in computational mechanics. For the simplest possible reference problems, the key is to have a cluster of at the low end of the spectrum. If the inputs, domain or material, are perturbed, the cluster breaks and tracing of the eigenpairs become difficult due to possible crossing of the modes. In this paper we have shown that the eigenvalue crossing can occur within clusters not only by perturbations of the domain, but also of material parameters. What is new is that in this setting, the crossing can be controlled; that is, the effect of the perturbations can actually be predicted. Moreover, the basis of the subspace is shown to be a well-defined concept and can be used for instance in low-rank approximation of solutions of problems with static loading. In our industrial model problem, the reduction in solution times is significant.Item Vuokratun liikennelentokoneen luovutus lentoyhtiöltä omistajalle(2010) Laaksonen, Mikael; Saarela, Olli; Insinööritieteiden ja arkkitehtuurin tiedekunta; Marquis, Gary