Chapter 245: Assignments

"... Therefore, the Helmholtz equation is bounded in a certain area. In the waveguide, due to the boundary conditions, the solution of the equation can be expressed by a linear combination of discrete eigenmodes."
"As for the compact difference format, it is even simpler. This is a high-precision finite difference method. For example..."
"However, the number of grid points involved in the difference format used to approximate the partial derivative at the discrete point xi is at least 1 larger than the order of the truncation error of this difference format... Also, it shows that the difference format has serious numerical dispersion The compact difference format is different from the above-mentioned display difference format. It uses the weighted average of the function values ​​at several points near the grid point xi to approximate the weighted average of the partial derivatives of the function at several grid points near the xi point."
Cheng Nuo talked about his opinions to the three of them like a treasure. The three people on the side were dumbfounded.
In the end, Cheng Nuo raised his head very humbly to Wang Genji, with an attitude of sincerely wanting to ask for advice, "Senior, these things are just a little bit of my humble opinion. There must be many shortcomings, and I hope that the seniors can enlighten me."
Wang Genji: "..."
Enlighten me? Please enlighten me with a yarn!
Wang Genji looked at Cheng Nuo with speechless eyes at this time. The wind was messy and he didn't know what to say.
"Helmholtz equation" and "compact difference format" are the two most important keywords for their project.
In fact, before the topic was put in their hands, Wang Genji, a junior in the college, had only slightly heard of these two rankings.
That's the kind that I've heard a little bit, and only heard the name. It is not that Cheng Nuo's "slightly heard" pretending style.
To be honest, Wang Genji was even suspicious. In the concept of the two, the level represented by a little hearing is completely different.
The whole lot of things that Cheng Nuo said could not be summed up in the words "slightly heard".
Cheng Nuo was there for more than ten minutes, but Wang Genji listened carefully all the time.
It can be said that what Cheng Nuo said is not a single mistake, but also very comprehensive. Even some things, Wang Genji, who has been studying this subject for more than a month, did not understand.
As for enlightenment...
Wang Genji had a bitter face and looked at his other two comrades as if asking for help.
Help, brothers!
The two of them didn't seem to feel Wang Genji's eyes the same.
Zhuang Poxiao: "Brother, let's go to the first floor of the cafeteria for lunch. I heard that there is a new optional window there, and the taste is not bad."
Jiang Shuobo: "Well, this is not bad. We will go there together in a while."
Wang Genji: "Hehe..."
What about the good friendship?
"Genji senior, are you okay?" Cheng Nuo asked Wang Genji's constipated expression aloud. "Actually, I have a few bottles of Kidney Treasure in my dormitory. Or I will bring you next time. Liuwei Dihuang Wan also has them."
"..." Wang Genji waved his hand, "I'm fine, let's continue."
Wang Genji turned around, carrying his hands on his back, with an unpredictable look, "In fact, all you know about these two terms is just a fur. I won't say anything about it. Because even if I said it, you still I am afraid it will be difficult to understand in a half-time. I have never advocated a duck-filling education."
"So, during the next period of time, you will follow the three of us to study this project. It is estimated that after the end of the project, you will have a deeper understanding of the two terms."
Cheng Nuo's standard adorable new student nodded obediently, "Okay, senior."
Good risk, the senior's face was finally saved.
Wang Genji wiped the sweat from his forehead.
"Then senior, what is my specific task?" Cheng Nuo asked, and then added, "Right, there is still the research progress on this subject?"
Wang Genji turned around, sat opposite Cheng Nuo, scratched his head, and said in embarrassment, "This is more than a month, because the three of us are busy with other things. At present... we are just drawing the general framework of this project. Build it up."
"As for the specific content filling, if you calculate according to the progress, it is less than...5%."
Cheng Nuo rolled his eyes, expressing speechlessness.
The progress is one twenty tenths!
The scientific research time of this project, when fully calculated, is less than five months. More than a month has passed, but the progress of the subject is currently only 5%.
It seems that in the later time, everyone wants to go home for a good year, and it is almost impossible not to burst the liver.
As the deputy leader of this research group, Jiang Shuobo coughed slightly and spoke slowly.
"Today the four of us got together, and the busy time of the three of us should have passed. And Cheng Nuo, you are now in your freshman year and you have plenty of spare time."
"Then now, I will divide the subject for everyone."
Such a complicated project is naturally not done by one person from start to finish. Division of labor and cooperation and mutual coordination are very necessary at this time.
Jiang Shuobo turned his head and said to Cheng Nuo, "I just said the basics, and we have completed the general framework of this project."
"This project can actually be divided into five parts."
"The first part, and the most basic part, is to obtain the linear system of the two-dimensional he1mho1tz equation through the one-dimensional he1mho1tz equation combined with the compact difference scheme. Cheng Nuo, this is the simplest part of the five parts. ,is that OK?"
Cheng Nuo nodded, "No problem."
"The second part is the correction of the coefficient matrix of UU reading www.uukanshu.com, that is... this part is left to you to do. You are the best at this aspect."
"Don't worry, leave it to me." Wang Genji patted his chest.
"The third part is the calculation of loop preconditioners and convergence analysis."
"The fourth part, use the preprocessing system to solve the algorithm."
"Part five, experiment with numerical values."
"The three parts of three, four and five can be combined into one, and I will study with Daxiao."
Zhuang Poxiao nodded and agreed.
"Time is tight and the task is heavy. I hope we can all be motivated and strive for the upper end! Strive for an early presentation of the results of the project."
"Come on!"
The palms of the four people were stacked together, cheering on.
"Senior, well, can I ask a more tacky question?" Cheng Nuo said.
"speak."
"How much is the research funding for our subject?"
"Ten thousand. To be precise, it is ten thousand and seventy-one dollars."
Cheng Nuo: "..."
How can this be so odd? !
"No, we belong to a national-level project anyway, so just a little funding?"
"It's good to have funds. Our subject is a pure mathematics project. We use mathematical methods to solve mathematical problems. There is no such thing as a physical chemistry subject to burn money. It is good to be able to give so much."
"By the way, I forgot. I will come up with a thousand yuan from the research fund in a moment, Cheng Nuo, you will go to the bookstore with Genji in the afternoon and buy all the books on this list."
Jiang Shuobo waved his hand with a look of wealth.
"When we are doing projects, we have to look like doing projects. It is not convenient to go to the library to borrow books all the time. Since there is no money elsewhere, then go...buy books!
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