"Pretreatment method for joint compact differential discrete equation systems of two-dimensional helmholtz equations"!

This is the full name of this project. It is very long and very twisted.

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

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

It is an elliptical partial differential equation describing electromagnetic waves, named after the German physicist Helmholtz, and is usually found in studies of physical problems involving partial differential equations that have both spatial and time dependencies.

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

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

Among them, △ is the Laplace operator, k is the wavenumber, the closed set Ω∈r^d, d=1,2,3...

There are many numerical solutions to the helmholtz equation, mainly including finite difference method, finite element method, boundary element method and gridless method. However, the above requirements for derivatives are high and the calculation amount is relatively large.

Therefore, this research project is to disperse the helmholtz equation through the joint compaction difference format (ccd). The values ​​of the helmholtz polynomial at two extremely adjacent points at each point and the first and second derivative values ​​are combined with the Taylor expansion to derive the linear system.

Simply put, this is a very complex and extremely proof of computing power.

Compared with some of the exercise questions that Cheng Nuo and the others saw, they are not on the same level of difficulty. Therefore, they need to apply for a topic specifically and spend a lot of time studying this issue.

At Cheng Nuo's exclamation, Liao Zhixing smiled undeniably, "Indeed, this project is indeed a bit difficult for you at present. However, it is not impossible to complete."

"What's more, it's not that you need to complete this task alone. Instead, this small team composed of four of you has to cooperate with each other. Each of them uses their strengths and devote themselves to their studies."

Finally, Liao Zhixing said in a serious voice, "You must always remember one sentence: Those who have ambition will succeed, and those who have ambitions will be able to end their boats. Two hundred Qin Passes will eventually belong to Chu. Those who work hard will never let go will be punished. If you sleep in firewood and taste gall, three thousand Yue Jia can swallow Wu!"

After filling the four of them with a bowl of chicken soup, Liao Zhixing picked up the thermos cup on the table and took a sip.

He raised his wrist, looked at the time on his watch, and then stood up.

"Okay, I have something to do here. I'll leave it to you here. Jiang Shuobo, Wang Genji, and Zhuang Poxiao, please introduce the main content of this topic to Cheng Nuo and your current research progress. Then find something for Cheng Nuo. You can discuss what you want to do.

"Okay." The three seniors nodded and watched Liao Zhixing push the door and leave.

In the office, the atmosphere was silent for a few minutes.

Senior Jiang Shuobo smiled softly, "Don't be so silent. Basically, tell this junior Cheng Nuo about the topic we are doing. Let him have a rough idea of ​​what we are doing."

"No problem." Wang Genji snapped his fingers, took out his laptop from his schoolbag, connected to the projector in the office, and raised his eyebrows at Cheng Nuo, "Senior Brother Cheng Nuo, look at your confused little eyes, you must have eyes darkened at this topic."

"But it doesn't matter. You are just a freshman, and your knowledge reserves are obviously not enough. You don't need to understand this topic thoroughly. Let us have the three of the difficulties. You just need to help us."

"I'm here with senior, I promise to take you to show off and fly!" Wang Genji patted his chest and said this sentence in full pretentious breath.

"Basics, stop talking nonsense, hurry up and talk. Then we will assign the task and it will be dispersed." Jiang Shuobo held his glasses and urged.

"Okay, right now, right now!" Wang Genji controlled the mouse and clicked on an ord document.

He coughed lightly and spoke slowly, "In fact, to put it simply, our topic is to discrete the two-dimensional helmholtz equation using the compact difference format. This difference format has the characteristics of sixth order accuracy, three-point difference and implicit..."

Halfway through the sermon, Wang Genji seemed to suddenly remember something and asked Cheng Nuo, "Senior Cheng Nuo, you should know what the helmholtz equation and the compact difference format are? It seems that you have not yet touched these two nouns."

"However, since Teacher Liao asked you to join our research team, it should not be a problem for you, right?" Wang Genji looked at Cheng Nuo with a smile.

"Do you have a helmholtz equation and a tight difference format?" Cheng Nuo scratched his head and said modestly, "I heard a little."

"Oh?" Wang Genji's eyes lit up and he stretched out his hand to signal Cheng Nuo, "Senior Cheng Nuo, please briefly explain your understanding. Just take this opportunity to take advantage of the senior to add to you what you missed, so you have a thorough understanding of these two terms."

In Wang Genji's view, it is not easy to know these two nouns that obviously exceed the scope with Cheng Nuo's freshman year. It is probably just a chance to hear it. In the end, it is not up to me to explain it myself.

Just so happened that Wang Genji planned to take this opportunity to establish the prestige of his senior in Cheng Nuo's heart.

"Then I would like to thank the senior for this. Please give me a sincere tone." Cheng Nuo said.

"Oh, it's not trouble, it's not trouble." After receiving Cheng Nuo's praise, Wang Genji waved his hand and laughed proudly, "Teachering my juniors' studies is the matter of our seniors. Just say boldly, it doesn't matter if you say it wrong!"

Cheng Nuo nodded, "Then let me talk about the helmholtz equation first. It is named by the German physicist Helmholtz. It refers to a hyperbolic partial differential equation with the form of (△2+k2)ψ=f in mathematical form,... In the formula, △2 is the Laplace operator, and in the Cartesian coordinate system, the Helmholtz equation, the Helmholtz equation; ψ is the function to be found; k2 is the constant; f is the source function. When f is equal to zero, it is called the homogeneous Helmholtz equation; when f is not equal to zero, it is called the non-homogeneous Helmholtz equation..."

Cheng Nuo talked freely: "...When a function f(x,y,z,t) changes in a simple harmony over time, it can be represented as f(x,y,z)ejt. At this time, д/дt is equivalent to j, д2/дt2 is equivalent to -2, substituting..."

From the source, formula, solution, transformation, and application of the Helmholtz equation, Cheng Nuo can be said to be comprehensive. Every place is meticulous and cannot find any mistakes.

Cheng Nuo talked for more than ten minutes alone, saying that helmholtz equation is a trend that has not stopped.

Wang Genji, who was sitting opposite Cheng Nuo, had already grown his mouth in disbelief.

Have you heard of it?

I just believed in your evil words at the beginning.

This is called a little hearing, so what do we mean?
Chapter completed!