Omnipotent Data

A genius remembers the address of this site in one second: (Vertex Chinese), the fastest update! No ads! "Preprocessing method for joint compact differential discrete equations of two-dimensional helmholtz equation"!

This is the full name of this project. Very long and convoluted.

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

Because of its relationship with the wave equation, the equation has a wide range of applications in related research fields such as electromagnetic radiation in physics, seismology and acoustics.

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

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

There are many numerical solutions for helmholtz equation, mainly including finite difference method, finite element method, boundary element method and meshless method. However, the above several have higher requirements for derivatives and a relatively large amount of calculation.

Therefore, this research project is to discretize the Helholtz equation through the joint compact difference scheme (ccd). Combine the value of the helmholtz polynomial at each point and two adjacent points with the value of the first and second derivatives to derive the linear system combined with the Taylor expansion.

To put it simply, this is a very complex and extremely computationally challenging subject project.

Compared with some practice questions that Cheng Nuo and others have seen, they are not at a level of difficulty at all. Therefore, it is necessary to declare a subject specifically and spend a lot of time studying this issue.

To Cheng Nuo's exclaim, Liao Zhixing smiled and nodded, "Indeed, this project is indeed a bit difficult for you now. However, it is not impossible to complete."

"What's more, it's not that you are required to complete this task alone. Instead, it depends on the small team of four of you to cooperate with each other. Each exerts its own strengths. With great concentration."

Finally, Liao Zhixing said solemnly, "You must always keep in mind this sentence: Those who have aspirations, things will come true, the two hundred Qinguans will ultimately belong to Chu. People who work hard, the sky will not fail, the salary and the courage, three thousand more can swallow Wu! "

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

He raised his wrist and checked the time on his watch. Then got up and stood up.

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

"Good." 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 senior Jiang Shuobo smiled soothingly, "Don't be so silent. Basically, you can tell this student Cheng Nuo about the subject we are doing. Let him know what we are doing."

"No problem." Wang Genji snapped his fingers, took out his laptop from his schoolbag, connected it to the projector in the office, and raised his eyebrows at Cheng Nuo, "Cheng Nuo, look at your confused little eyes, It must be a black eye on this subject."

"But it doesn't matter, you are just a freshman, and the knowledge reserve is obviously not enough. This topic does not require you to be able to understand him. The difficult ones, let us three. You only need to give us a hand."

"I have a senior, I promise to take you to pretend to take you to fly!" Wang Genji patted his chest, pretending to be full of breath.

"Basics, don't talk nonsense, you hurry up. Then we will assign a task and we will be gone." Jiang Shuobo urged while helping his glasses.

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

He coughed slightly, and slowly said, "Our subject, in fact, is to use compact difference format to discretize the two-dimensional helmholtz equation. This difference format has sixth-order precision, three-point difference and implicit specialty……"

Halfway through the preaching, Wang Genji seemed to remember something suddenly, and asked Cheng Nuo, "School brother Cheng Nuo, you should know what the Helholtz equation and the compact difference format are? These two terms seem to be yours. Haven't touched Tao yet."

"However, since Teacher Liao asked you to join our research group, it shouldn't be a problem for you?" Wang Genji looked at Cheng Nuo with a smile.

"Helholtz equation and compact difference format?" Cheng Nuo scratched his head and said modestly, "I heard it slightly."

"Oh?" Wang Genji's eyes lit up, and he stretched out his hand to signal Cheng Nuo, "Then Junior Cheng Nuo, you can briefly talk about your understanding. Just taking advantage of this opportunity, the senior will give you something you missed. Understand these two terms."

In Wang Genji's view, with Cheng Nuo's freshman degree, it is not easy to know these two obvious super-class terms. I probably heard it by accident. In the end, I still have to explain it myself.

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

"Then thank you senior~www.readwn.com~ trouble you." Cheng Nuo said sincerely.

"Hey, no trouble, no trouble." After receiving Cheng Nuo's compliment, Wang Genji waved his hand and laughed triumphantly. "Guiding students to study is what we belong to as seniors. You 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 the hyperbolic deviation of the form (△2+k2)ψ=f mathematically. Differential equation, ... where △2 is Laplace operator, Helmholtz equation is Helmholtz equation in Cartesian coordinate system; ψ is the function to be determined; k2 is constant; f is the source function. When f is equal to zero, it is called homogeneous Helmholtz equation; when f is not equal to zero, it is called non-homogeneous Helmholtz equation..."

Cheng Nuo talked freely: "... When a function f(x, y, z, t) changes with time, it can be expressed in the form of f(x, y, z) ejt, then д/дt It is equivalent to j, and д2/дt2 is equivalent to -2, substitute in..."

From the sources, formulas, solutions, transformations, and applications of Helmholtz equations, Cheng Nuo can be said to be comprehensive. Everywhere, he speaks nuancedly and can't pick up any mistakes.

Cheng Nuo talked about the term helmholtz equation alone for more than ten minutes. What he said was a spit, circumflex and frustration, and it has not stopped until now.

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

Slightly heard?

I believed your evil in the first place, so I believed your nonsense.

This is a slightly heard word, then what are we?

Does this guy have any misunderstandings about this word? Mobile users please browse and read for a better reading experience.