Development of highly convergent numerical algorithms for short elastic wave simulation

Wednesday, August 30, 2017 - 14:00
Dissertation Defence Hall (K. Donelaičio St. 73- 403 room)

Author, Institution: Andrius Kriščiūnas, Kaunas University of Technology

Science Area, Field of Science: Physical Sciences, Informatics – 09P

Summary of the Doctoral Thesis: Summary

Scientific Supervisor: Prof. Dr. Habil. Rimantas BARAUSKAS (Kaunas University of Technology, Physical Sciences, Informatics – 09P).

Dissertation Defence Board of Informatics Science Field:
Prof. Dr. Habil. Minvydas Kazys RAGULSKIS (Kaunas University of Technology, Physical Sciences, Informatics – 09P) – chairman;
Prof. Dr. Habil. Gintautas DZEMYDA (Vilnius University, Physical Sciences, Informatics – 09P);
Prof. Dr. Habil. Rimantas KAČIANAUSKAS (Vilnius Gediminas Technical University, Technological sciences, Mechanical engineering– 09T);
Prof. Dr. Alfonsas MISEVIČIUS (Kaunas University of Technology, Physical Sciences, Informatics – 09P);
Prof. Dr. Miguel A. F. SANJUAN (Rey Juan Carlos University, Physical Sciences, Informatics – 09P).

The doctoral dissertation is available on the internet and at the libraries of Kaunas University of Technology (K. Donelaičio St. 20, Kaunas, Lithuania) and Vytautas Magnus university (K. Donelaičio St. 52, Kaunas, Lithuania).

Annotation:

The propagation of waves in elastic or acoustic media is mathematically formulated as linear partial differential equations of continuum mechanics, which can be numerically solved by discretization in space and time. Though mathematically and programmatically simple, numerical wave propagation models still have an inherent “weak spot”. They tend to distort the shapes of propagating waves when the space step of the computational grid is too big. Therefore, the most important problem arising in numerical simulations of short wave propagation is a very high demand for computing resources in case waves are short compared to the dimensions of the computational domain. A new algorithm based on the modal synthesis approach of optimally corrected modes has been developed in this work. This enabled to obtain the finite element models of significantly broader close-to-accurate modal frequency range compared to earlier models. Although the principal approach to the element synthesis was known before, its main drawback has been overcome in this work. The mass matrices of the new elements are diagonal and can be directly applied in numerical schemes of explicit dynamic analysis.