Implement high-precision conjugate gradient solver for improved WebGPU performance

[Copilot]

This PR addresses the precision issues in the WebGPU implementation by introducing a comprehensive linear system solver framework with a high-precision conjugate gradient method.

Problem

The existing solver implementation lacked precision for conjugate gradient operations, particularly affecting WebGPU-accelerated computations in finite element analysis scenarios.

Solution

Implemented a centralized linear system solver architecture with multiple high-precision algorithms:

Key Components Added

1. Centralized Linear System Solver (linearSystemSolverScript.js)

• Unified interface supporting lusolve, jacobi, and cg/conjugate methods
• Consistent error handling and performance logging
• Easy extensibility for future solver implementations

2. High-Precision Conjugate Gradient Solver (conjugateGradientSolverScript.js)

• Optimized for symmetric positive definite systems common in FEA
• Uses native Float64 arithmetic for maximum precision
• Implements classical CG algorithm with proper convergence checking
• Significantly faster convergence compared to iterative methods like Jacobi

3. Enhanced Jacobi Solver (jacobiSolverScript.js)

• Clean JavaScript implementation replacing complex async Taichi.js wrapper
• Maintains interface consistency with other solvers
• Improved numerical stability through better iteration management

4. Helper Utilities (helperFunctionsScript.js)

• Euclidean norm calculation for convergence testing
• System size calculation utilities
• Foundation for future numerical operations

Integration Improvements

• Updated FEAScript.js to use the new centralized solver system
• Modified newtonRaphsonScript.js to leverage improved linear system solving
• Enhanced build configuration with mathjs dependency for mathematical operations

Performance Benefits

The conjugate gradient implementation provides superior precision through:

• Faster Convergence: CG typically converges in O(√κ) iterations vs O(κ) for Jacobi, where κ is the condition number
• Theoretical Optimality: CG is provably optimal for symmetric positive definite systems
• Reduced Error Accumulation: Fewer iterations mean less floating-point error accumulation
• Better Numerical Stability: Superior handling of ill-conditioned matrices

Testing

• ✅ Build system integration verified
• ✅ All solver methods properly integrated with FEAScriptModel
• ✅ Backward compatibility maintained for existing code
• ✅ Support for both "cg" and "conjugate" method names

Example Usage

const model = new FEAScriptModel('solidHeatTransfer', meshConfig, boundaryConditions);
model.setSolverMethod('cg'); // Use conjugate gradient for faster, more precise solving
const result = model.solve();

This implementation provides a solid foundation for high-precision numerical computations in WebGPU-accelerated finite element analysis while maintaining full backward compatibility with existing solver methods.

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[nikoscham]

@sridhar-mani could you please review this pull request? Also, I have performed some major updates to the core (see #40). I really appreciate your effort! One small request though: for major tasks (like implementing an entire issue), could you please avoid relying entirely on AI copilots? I’d like the codebase to retain a more “human” touch, as I believe human-written code can often be more efficient. This applies to the other two pull requests as well..

[sridhar-mani]

@sridhar-mani could you please review this pull request? Also, I have performed some major updates to the core (see #40). I really appreciate your effort! One small request though: for major tasks (like implementing an entire issue), could you please avoid relying entirely on AI copilots? I’d like the codebase to retain a more “human” touch, as I believe human-written code can often be more efficient. This applies to the other two pull requests as well..

Yeah that is my intention too. I was just excited to see how much the model is able to handle vague and niche prompt and i was just testing. Didn't hope it would alarm you. ;-)

[nikoscham]

@sridhar-mani could you please review this pull request? Also, I have performed some major updates to the core (see #40). I really appreciate your effort! One small request though: for major tasks (like implementing an entire issue), could you please avoid relying entirely on AI copilots? I’d like the codebase to retain a more “human” touch, as I believe human-written code can often be more efficient. This applies to the other two pull requests as well..

Yeah that is my intention too. I was just excited to see how much the model is able to handle vague and niche prompt and i was just testing. Didn't hope it would alarm you. ;-)

Thanks for your reply @sridhar-mani ! No worries — I understand you were experimenting with what the model could do. It did produce some interesting results though. When you have time, feel free to merge what you think fits into the feature/webGPU branch (this was formerly webGPU, which I’ve renamed), once you’ve synced it with the latest main branch.

In the future, I propose to follow the branch-naming rules that are described here https://github.com/FEAScript/FEAScript-core/blob/main/CONTRIBUTING.md (e.g. feature/topic). This should help keep things tidy - hope I’m not overloading you with rules!
(I’ve also renamed readers to feature/readers - couldn’t resist tidying it up! 😄)

Now in order to update the branch name in your local environment you should (according to github):

  git branch -m webGPU feature/webGPU
  git fetch origin
  git branch -u origin/feature/webGPU feature/webGPU
  git remote set-head origin -a

And do also the corresponding commands for feature/readers

Please let me know once you’ve finished so I can delete the pull requests created by Copilot.

[sridhar-mani]

@sridhar-mani could you please review this pull request? Also, I have performed some major updates to the core (see #40). I really appreciate your effort! One small request though: for major tasks (like implementing an entire issue), could you please avoid relying entirely on AI copilots? I’d like the codebase to retain a more “human” touch, as I believe human-written code can often be more efficient. This applies to the other two pull requests as well..

Yeah that is my intention too. I was just excited to see how much the model is able to handle vague and niche prompt and i was just testing. Didn't hope it would alarm you. ;-)

Thanks for your reply @sridhar-mani ! No worries — I understand you were experimenting with what the model could do. It did produce some interesting results though. When you have time, feel free to merge what you think fits into the feature/webGPU branch (this was formerly webGPU, which I’ve renamed), once you’ve synced it with the latest main branch.

In the future, I propose to follow the branch-naming rules that are described here https://github.com/FEAScript/FEAScript-core/blob/main/CONTRIBUTING.md (e.g. feature/topic). This should help keep things tidy - hope I’m not overloading you with rules! (I’ve also renamed readers to feature/readers - couldn’t resist tidying it up! 😄)

Now in order to update the branch name in your local environment you should (according to github):

  git branch -m webGPU feature/webGPU
  git fetch origin
  git branch -u origin/feature/webGPU feature/webGPU
  git remote set-head origin -a

And do also the corresponding commands for feature/readers

Please let me know once you’ve finished so I can delete the pull requests created by Copilot.

No issues i am aware of the instructions but still thank you.