Chapter 241 (1/2)

Preprocessing method for two-dimensional Helmholtz equations with joint compact difference separation!

This is the full name of this project. It's very long and tongue twisty.

After hearing this, Cheng Nuo took a breath, ”this project is very difficult!”

The so-called Helmholtz equation, also known as Helmholtz equation.

It is an elliptic partial differential equation describing electromagnetic waves, named after Helmholtz, a German physicist. It usually appears in the study of physical problems involving both space and time dependent partial differential equations.

Because of its relationship with the wave equation, the equation is widely used in the fields of electromagnetic radiation, seismology and acoustics in physics.

The equation can be expressed as △ f (x) + K ^ 2F (x) = g (x), X ∈ Ω.

Where △ is Laplacian operator, K is wave number, closed set Ω∈ R ^ D, d = 1,2,3

There are many numerical methods for Helmholtz equation, including finite difference method, finite element method, boundary element method and meshless method. However, the above requirements for derivatives are higher and the amount of calculation is relatively large.

Therefore, this project is to discretize Helmholtz equation by combining compact difference scheme (CCD). By combining the values of Helmholtz polynomials at each point and the first and second derivative values, the linear system is derived by combining the Taylor expansion.

In short, this is a very complex and extremely test of computational power of the project.

Compared with some exercises that Cheng Nuo saw, they were not at a level of difficulty at all. So we need to apply for a project and spend a lot of time to study this problem.

For Cheng Nuo's exclamation, Liao Zhixing can't help but smile and nod, ”indeed, this project is really difficult for you at present. But it's not impossible. ”

”What's more, you are not required to complete this task alone. It's a small team of four of you working together. Each has its own advantages. Study hard. ”

Finally, Liao Zhixing said in a serious voice, ”you should always remember one sentence: if there is a will, there will be a way, and the two hundred Qinguan pass will eventually belong to Chu. If you work hard, you will live up to the sky. If you lie down on your salary and taste your courage, you can swallow Wu with 3000 Yue Jia! ”

After pouring a bowl of Chicken Soup for the four people, Liao Zhixing took the thermos cup in front of the table and took a sip.

He raised his wrist and looked at the time on his watch. Then get up and stand up.

”Well, I have something else to do. This way is for you. Jiang Shuobo, Wang Jiji and Zhuang duxiao will introduce the main contents of this project and your current research progress to Cheng Nuo. Then find something for Cheng Nuo to do. You can discuss it yourself

”Good.” The three elders nodded and watched Liao's trip push the door away.

In the office, there was silence for a few minutes.

Senior student Jiang Shuobo relaxed the atmosphere with a smile, ”don't be so silent. Foundation, you tell this student Cheng Nuo what we are doing. Give him a general idea of what we're doing

”No problem.” As soon as Wang Ji snapped his fingers, he took out his laptop from his schoolbag, connected it to the projector in the office, and raised an eyebrow at Cheng Nuo. ”Cheng Nuo, look at your confused little eyes, it must be a black eye on this subject.”