Browsing by Author "Hakula, Harri, Dr., Aalto University, Department of Mathematics and Systems Analysis, Finland"

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Demand-Responsive Transport: Models and Algorithms
(2013) Häme, Lauri
School of Science | Doctoral dissertation (article-based)
Demand-responsive transport is a form of public transport between bus and taxi services, involving flexible routing of small or medium sized vehicles. This dissertation presents mathematical models for demand-responsive transport and methods that can be used to solve combinatorial problems related to vehicle routing and journey planning in a transport network. Public transport can be viewed as a market where demand affects supply and vice versa. In the first part of the dissertation related to vehicle routing, we show how a given demand for transportation can be satisfied by using a fleet of vehicles, assuming that the demand is known at the individual level. In the second part, by considering the journey planning problem faced by commuters, we study how the demand adapts to the supply of transport services, assuming that the supply remains unchanged for a short period of time. We also present a stochastic network model for determining the economic equilibrium, that is, the point at which the demand meets the supply, by assuming that commuters attempt to minimize travel time and transport operators aim to maximize profit. The mathematical models proposed in this work can be used to simulate the operations of public transport services in a wide range of scenarios, from paratransit services for the elderly and disabled to large-scale demand-responsive transport services designed to compete with private car traffic. Such calculations can provide valuable information to public authorities and planners of transportation services, regarding, for example, regulation and investments. In addition to public transport, potential applications of the proposed methods for solving vehicle routing and journey planning problems include freight transportation, courier and food delivery services, military logistics and air traffic.
On Numerical Solution of Multiparametric Eigenvalue Problems
(2018) Laaksonen, Mikael
School of Science | Doctoral dissertation (article-based)
In 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.
On sparse tensor structures in lattice theory and applications of the polynomial collocation method based on sparse grids
(2017) Kaarnioja, Vesa
School of Science | Doctoral dissertation (article-based)
Due to the exponential increase in computational power ever since the invention of the computer, the use of tensors has become a more viable way to approach problems involving many variables. However, the efficient treatment of high-dimensional problems still requires special techniques such as tensor decompositions and utilizing sparsity. The first part of this dissertation considers the properties of symmetric meet and join tensors arising in lattice theory, which can be understood as generalizations of meet and join matrices such as classically studied GCD and LCM matrices, respectively. New low-parametric tensor decompositions are developed for general classes of lattice-theoretic tensors in both polyadic and tensor-train formats. The compressed representations endowed by these decompositions enable numerical computations involving high dimensionality and order, and the efficient application of tensor eigenvalue solution algorithms is studied for tensors belonging to these classes. The second part of this dissertation considers the application of sparse grid collocation algorithms for the solution of parameter-dependent partial differential equations involving high dimensionality. We consider as applications a class of stochastic eigenvalue problems and a parameter-dependent complete electrode model of electrical impedance tomography. A novel basis selection technique based on the maximum volume principle is introduced for multivariate polynomial interpolation over arbitrary node configurations.