This thesis concerns the solution of finite element discretised Laplacian eigenvalue problems of coupled systems. A relevant application is studying human speech, where vowels are classified according to the lowest resonant frequencies of the vocal tract during sustained pronunciation. When computing these frequencies, the acoustic environment has to be accounted for. In this thesis, the vocal tract is considered as an interior system that is coupled with its acoustic environment, the exterior system. The coupling occurs through a fixed interface. Models for computing the resonant frequencies are validated against data consisting of simultaneous MRI images and sound recordings. As the validation requires a large number of vocal tract geometries, an automatic extraction algorithm that generates vocal tract surface triangulations from MRI data is introduced. An instrument for performing frequency sweeps on physical models printed using these geometries was also modelled as a part of this thesis. The confined space inside the head coil of the MRI machine creates an acoustic environment where mixed modes appear. That is, standing waves that oscillate both inside the oral cavity and the head coil are formed. Hence, it is important that the acoustic environment consisting of the MRI coil is accurately modelled when validating computational models. To efficiently solve relevant resonances related to different vocal tract geometries coupled with the unchanging MRI head coil, a method for reducing the computational complexity related to the fixed exterior system is introduced. The mathematical observations related to the aforementioned method were generalised from an algebraic setting to a continuous Laplace eigenvalue problem. As a result, a theory for obtaining information on an eigenfunction in a local subdomain from localised boundary data was developed. The computational realisation of this theory is a domain decomposition type eigenvalue solver where tasks related to each subdomain are mutually independent. This method can be used to approximately solve finite element discretised eigenvalue problems where the number of degrees of freedom is prohibitively large for a single workstation to compute. Such an eigenvalue solver can be used to efficiently solve large eigenvalue problems without the need for a supercomputer. Due to the independence of computations related to subdomains, tasks can be sent over a network connection, making the method suitable for cloud computing environments.
|Translated title of the contribution||Kytkettyjen akustisten ominaisarvotehtävien ratkaiseminen|
|Publication status||Published - 2020|
|MoE publication type||G5 Doctoral dissertation (article)|
- domain decomposition