Omnipotent Data
Chapter 241
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."
"But it doesn't matter. You are only a freshman, and the knowledge reserve is obviously not enough. You don't need to be able to understand this subject. The difficult ones, give us three. You just need to give us a hand. "
"I'm here. I promise to take you and fly with you!" Wang Ji clapped his chest and pretended to be full of breath to say this sentence.
"Foundation, don't talk nonsense, you talk quickly. Then we assign the task and it's over. " Jiang Shuobo helped his glasses and urged him.
"All right, now, now!" Wang Ji controls the mouse and opens a word document.
He coughed and opened his mouth slowly. "Our project, in fact, is to use the compact difference scheme to discretize the two-dimensional Helmholtz equation. The difference scheme has the characteristics of sixth order accuracy, three-point difference and implicit
In the middle of the sermon, Wang Ji seemed to suddenly think of something. He asked Cheng Nuo, "you should know what Helmholtz equation and compact difference scheme are, don't you?"? These two nouns seem to have no contact with each other
"However, since Mr. Liao asked you to join our research group, it should not be a problem for you?" Wang Ji looks at Cheng Nuo with a smile.
"Helmholtz equation and compact difference scheme?" Cheng Nuo scratched his head and said modestly, "I've heard a little."
"Oh?" Wang Ji's eyes brightened, reaching for Cheng Nuo, "that Cheng Nuo's younger brother, tell me your understanding. Just take advantage of this opportunity, the elder will give you something you have missed. You can understand these two terms thoroughlyIn Wang Ji's opinion, with Cheng Nuo's freshman education, it is not easy to know these two terms which are obviously beyond the class. I guess I heard it by accident. In the end, it's not up to you to explain it yourself.
Just in time, Wang Ji plans to take advantage of this opportunity to build up the prestige of a senior student in Cheng Nuo's mind.
"Thank you very much. Please Cheng Nuo's tone is sincere.
"Oh, no trouble, no trouble." With Cheng Nuo's praise, Wang Ji waved his hand and laughed triumphantly, "it's our duty to guide students to learn. You can say it boldly, even if you say it wrong, it doesn't matter! "
Cheng nodded. "Let me first talk about the Helmholtz equation, which was named after Helmholtz, a German physicist. It refers to the hyperbolic partial differential equation with (△ 2 + K2) ψ = f in mathematics Where △ 2 is the Laplace operator, Helmholtz equation in rectangular coordinate system, ψ is the function to be solved, K2 is a constant, and 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 nonhomogeneous Helmholtz equation... "
Cheng Nuo talks with a lot of words When a function f (x, y, Z, t) changes harmoniously with time, it can be expressed in the form of F (x, y, z) ejwt. In this case, дддддддддддддддддддддд
From the source of Helmholtz equation, formula, solution, transformation, application, Cheng Nuo can be said to be all-round, every place said meticulous, can not pick out any mistakes.
Just for the term Helmholtz equation, Cheng has been talking about it for more than ten minutes. What he said is that there is a tendency of saliva flying and cadence, and it has not stopped until now.
Wang Ji, who is sitting opposite Cheng Nuo, has grown up incredibly at this time.
Have you heard anything about it?
I especially believe in your evil, will believe your lies.
It's called a little bit of hearing, so what are we?
This guy, is there any misunderstanding about this word?
www.mylovenovel.com , the fastest update of the webnovel!
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."
"But it doesn't matter. You are only a freshman, and the knowledge reserve is obviously not enough. You don't need to be able to understand this subject. The difficult ones, give us three. You just need to give us a hand. "
"I'm here. I promise to take you and fly with you!" Wang Ji clapped his chest and pretended to be full of breath to say this sentence.
"Foundation, don't talk nonsense, you talk quickly. Then we assign the task and it's over. " Jiang Shuobo helped his glasses and urged him.
"All right, now, now!" Wang Ji controls the mouse and opens a word document.
He coughed and opened his mouth slowly. "Our project, in fact, is to use the compact difference scheme to discretize the two-dimensional Helmholtz equation. The difference scheme has the characteristics of sixth order accuracy, three-point difference and implicit
In the middle of the sermon, Wang Ji seemed to suddenly think of something. He asked Cheng Nuo, "you should know what Helmholtz equation and compact difference scheme are, don't you?"? These two nouns seem to have no contact with each other
"However, since Mr. Liao asked you to join our research group, it should not be a problem for you?" Wang Ji looks at Cheng Nuo with a smile.
"Helmholtz equation and compact difference scheme?" Cheng Nuo scratched his head and said modestly, "I've heard a little."
"Oh?" Wang Ji's eyes brightened, reaching for Cheng Nuo, "that Cheng Nuo's younger brother, tell me your understanding. Just take advantage of this opportunity, the elder will give you something you have missed. You can understand these two terms thoroughlyIn Wang Ji's opinion, with Cheng Nuo's freshman education, it is not easy to know these two terms which are obviously beyond the class. I guess I heard it by accident. In the end, it's not up to you to explain it yourself.
Just in time, Wang Ji plans to take advantage of this opportunity to build up the prestige of a senior student in Cheng Nuo's mind.
"Thank you very much. Please Cheng Nuo's tone is sincere.
"Oh, no trouble, no trouble." With Cheng Nuo's praise, Wang Ji waved his hand and laughed triumphantly, "it's our duty to guide students to learn. You can say it boldly, even if you say it wrong, it doesn't matter! "
Cheng nodded. "Let me first talk about the Helmholtz equation, which was named after Helmholtz, a German physicist. It refers to the hyperbolic partial differential equation with (△ 2 + K2) ψ = f in mathematics Where △ 2 is the Laplace operator, Helmholtz equation in rectangular coordinate system, ψ is the function to be solved, K2 is a constant, and 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 nonhomogeneous Helmholtz equation... "
Cheng Nuo talks with a lot of words When a function f (x, y, Z, t) changes harmoniously with time, it can be expressed in the form of F (x, y, z) ejwt. In this case, дддддддддддддддддддддд
From the source of Helmholtz equation, formula, solution, transformation, application, Cheng Nuo can be said to be all-round, every place said meticulous, can not pick out any mistakes.
Just for the term Helmholtz equation, Cheng has been talking about it for more than ten minutes. What he said is that there is a tendency of saliva flying and cadence, and it has not stopped until now.
Wang Ji, who is sitting opposite Cheng Nuo, has grown up incredibly at this time.
Have you heard anything about it?
I especially believe in your evil, will believe your lies.
It's called a little bit of hearing, so what are we?
This guy, is there any misunderstanding about this word?
www.mylovenovel.com , the fastest update of the webnovel!