Testing Of Multiscale Finite Element Method

1.

Testing Of Multiscale Finite Element Method
Thesis defender: Cao Ziheng(Цао Цзыхэн)
Scientific Advisor: K.A.Nadolin (Надолин Константин Аркадьевич)

2.

Content
1
•Background and significance
2
•Research content
3
•Research process
4
•Research conclusion
5
•Summary

3.

Background and significance
——1.Background
——2.Significance
1

4.

1. Background and significance
Background
Stones in the soil, Steel in cement wall, components made of
different materials and so on, "Inhomogeneity" exists in various forms
in nature and industry. For the modeling and analysis of
inhomogeneous objects or regions, mathematical models with large
differences in parameters ​are usually established. At the same time, we
use a new method for such problems: multi-scale finite element
method.

5.

1. Background and significance
Significance
The multiscale finite element method is a method that obtains the
approximate solution by dividing mesh in multiscale way and
applying the finite element method to each scale mesh, it is
significantly different from the classical finite element method. I think
it is necessary to describe the implementation of the multi-scale FEM
through examples and to explore the advantages and disadvantages of
the classical FEM and the multi-scale FEM through comparison.

6.

Research content and targets
——1.Content
——2.Targets
2

7.

2. Research content and targets
The research content is the implementation of
the multi-scale finite element method for a strongly
regular inhomogeneous 2-D plane plate’s Poisson
equation problem, including theory and computer
program, as well as comparation experiments in
three different aspects and conclusion.

8.

2. Research content and targets
Implementation process of
Target 1
multiscale finite element method.
Comparison of classical and
Target 2
Target 1
multiscale finite element methods
Target 2

9.

Research Process
——Example introduction
——Theoretical process
——Matlab implementation
——Comparation experiments
3

10.

3. Research process
Example introduction
We list an example of Poisson's equation problem on strongly regular
inhomogeneous two-dimensional plane plate. The flat plate region is