They're already in university, and the primary school system is only just starting out?

You understand now?

Has the gap between people really gotten this big?

Sun Yu himself, a proper graduate student in applied mathematics, spent two whole days studying the plan and related materials before he could barely understand the logic and the limitations of existing calculation methods.

And can this "CL" on the other side really understand after just looking at the document and listening to me explain it once?

No way! This is a genius I hired at a cost of 2000 yuan. What if he misunderstands the direction and gives a completely different solution? Wouldn't my money be wasted?

Thinking of this, Sun Yu quickly spoke up, trying to be as tactful as possible, attempting to remind the other party: "Well, there are a few parts in this plan that are a bit complicated, so perhaps I could..."

Before he could finish speaking, the voice in the earpiece ignored him and continued talking.

"A typical structural stability analysis. You used industry-standard finite element software for buckling analysis. At its core, it is to solve a generalized eigenvalue problem: ([K]-λ[KG]){φ}= 0."

The sound of "CL" was neither hurried nor slow.

Sun Yu's mouth, which he was about to open, froze in mid-air.

Because what the other party said is completely correct.

The voice continued, "Based on your description and the data in the document, the difficulty you're facing lies in the critical buckling factor λ, which is the solution you're looking for. Theoretically, it should be within a relatively clear range. I see in the document that it's 4.0 ± 0.3."

"But the results of your software's repeated calculations are sometimes as low as 3.2, and sometimes they jump to 4.8 for no reason. The results are divergent and cannot be stably converged to the theoretical expected range."

Sun Yu was completely dumbfounded.

He discovered that he was the only clown.

I may have used up all the luck of my first half of life to encounter a genius of "CL" level. I actually tested this genius's true strength with undergraduate math problems first, and then doubted whether he could understand my explanation of the solution in one go.

Sun Yu raised his hand and slapped himself lightly.

Then, like a thief, he quickly moved the mouse to mute himself.

CL's voice is indeed very youthful, and you can't hear any of the fatigue that comes with years of working.

But to Sun Yu now, the voice sounded eerily calm.

He seemed indifferent to what he was saying, as if he were mechanically reading from a script.

"...So, the essence of the problem is clear. Your existing solver exhibits numerical instability when dealing with eigenvalue clustering or ill-conditioned matrix problems. What you need from me is a completely new algorithm with better numerical stability that can accurately solve for the minimum eigenvalue you want."

As soon as he finished speaking, Sun Yu saw the gray "CL" avatar on the meeting interface suddenly light up.

He turned on the camera.

Sun Yu's heart stirred, and he curiously turned his gaze to the small video window.

However, the face of the genius he had imagined did not appear in the picture.

The camera was adjusted to point directly at a clean, blank draft paper laid out on the table.

Immediately afterwards, a hand holding a pen appeared in the picture.

"CL" was written down while explaining to Sun Yu.

"I've designed a hybrid approach, which will be implemented in several steps."

"The first step, for your generalized eigenvalue problem [K]x =λ[KG]x, is to construct an efficient preconditioner [M] to improve the spectral properties of the coefficient matrix."

The pen tip flew across the paper.

"Here, I suggest using a preconditioning technique based on incomplete Cholesky decomposition or algebraic multigrid (AMG) directly applied to your stiffness matrix [K]. Because, based on your data, the [K] matrix is ​​typically a well-defined positive definite matrix..."

"The second step is to use a solution algorithm that is more robust to ill-conditioned problems and eigenvalue clustering."

"I recommend using the Jacobi-Davidson method. Compared to what you're currently using, or the more traditional Lanczos method or subspace iteration method, it has less dependence on the initial guess vector..."

"The third step is to further improve the accuracy and efficiency of solving for the minimum eigenvalues. We need to combine spectral transformation techniques."

"Within the Jacobi-Davidson framework, apply a shift-and-invert transformation. Choose a shift σ that is close to your expected minimum eigenvalue λ_cr; in your problem, this means choosing σ=4.0. This transforms the original problem into solving a more manageable standard eigenvalue problem..."

"Finally, there's adaptive adjustment. Regarding the grid sensitivity issue you mentioned, key parameters within the algorithm, such as convergence tolerance and subspace dimension, should be adaptively adjusted based on the estimation of the local condition number of the matrix, rather than using fixed values."

"At the same time, during the algorithm's operation, the rate of change of the residual norm and eigenvalue estimates must be monitored in real time. Once convergence stalls are detected, the preconditioners must be dynamically updated immediately..."

At this point, the A4 draft paper was already densely covered with various variables and formulas.

Sun Yu's eyes were fixed on the screen, but his brain had already stopped working.

Suddenly, Sun Yu was startled.

who am I?Where am i?

The person on the other end was talking about many terms and knowledge points that he seemed to have seen or heard during his graduate studies, but when put together, they were like gibberish to him.

However, none of this matters anymore.

He has now determined that the mathematical level of the person opposite him, "CL," has reached a level that he cannot comprehend at all and can only admire.

That's enough!

All I need to do is cling to this powerful figure, and everything will be fine!

Just then, the video window went dark; "CL" had turned off the camera.

He continued, "I've written down the core algorithm steps and key formulas on that draft paper. What you need to do now is take the time to understand them thoroughly, then organize these steps into pseudocode, find a programmer from your company to help you implement a script, and finally integrate this script into your finite element software."

Sun Yu: What? I'm going to deal with Tang Sanzang and his disciples?

Sun Yu quickly said, "No, no, no, please help me put together some pseudocode. The time isn't up yet anyway."

Fearing rejection, he quickly added, "Look, look at the time. Our consultation starts around 10 a.m., and it's not even 11 a.m. yet. Your three-hour package still has plenty of time!"

Sun Yu now feels that expensive things are all good except for their price!

There was a brief silence on the other end of the earphone.

"Okay, just a moment."

A few minutes later, a file sharing prompt appeared on the meeting's sharing interface.

"CL" shared two pictures.

Sun Yu downloaded and examined the files, which included the previous draft paper with algorithm steps and key formulas, as well as pseudocode newly written by "CL".

Sun Yu felt that a heavy burden had finally been lifted from his heart.

He glanced at the time; it was already 11:30.

I quickly said in the meeting via voice message, "Master, I'll tidy up this myself. It's getting late, you should get some rest."

A youthful voice came from the other end: "Okay, I'll log off now. I've recorded the time; there are 83 minutes left. Please contact me 3 days in advance to schedule your next consultation."

Then Sun Yu saw "CL" leave the conference room.