Awesome

Taichi-BEM

----------Analytical(Left)----Solved(Middle)----Difference(Right)

Laplace Equation (2D)

cd demo
python demo_Laplace.py --dim 2 --boundary Dirichlet --object disk --GaussQR 5 --scope Interior

Laplace Equation (3D)

cd demo
python demo_Laplace.py --dim 3 --boundary Dirichlet --object sphere --GaussQR 5 --scope Interior

Helmholtz Equation (3D)

cd demo
python demo_Helmholtz.py --dim 3 --boundary Dirichlet --object stanford_bunny --GaussQR 5 --scope Interior

Helmholtz Transmission Equation

cd demo
python demo_Helmholtz_Transmission.py --dim 3 --boundary Full --object sphere --GaussQR 5

Norm analysis (Still Working on! 👨‍💻)

• The sample step of wave number is 1/30, which implies for wavenumbers between [16, 18], 60 points are sampled.
• Precious matters, float64 shows more stability than float32 for operator AI (Somehow not very obvious for operator AII).

The norm of A & Augmented A of sphere

<img src="demo/Physical_Augment_A1_plot_1_1_sphere_GaussQR4.png" height="192"> <img src="demo/Physical_Augment_A2_plot_1_1_sphere_GaussQR4.png" height="192">

<img src="demo/NonPhysical_Augment_A1_plot_1_1_sphere_GaussQR4.png" height="192"> <img src="demo/NonPhysical_Augment_A2_plot_1_1_sphere_GaussQR4.png" height="192">

As well as the norm of A & Augmented A of stanford bunny

<img src="demo/Physical_Augment_A1_plot_1_1_stanford_bunny_GaussQR4.png" height="192"> <img src="demo/Physical_Augment_A2_plot_1_1_stanford_bunny_GaussQR4.png" height="192">

<img src="demo/NonPhysical_Augment_A1_plot_1_1_stanford_bunny_GaussQR4.png" height="192"> <img src="demo/NonPhysical_Augment_A2_plot_1_1_stanford_bunny_GaussQR4.png" height="192">

How to run the code

cd taichi-BEM
conda create -n ti-BEM python=3.8
conda activate ti-BEM
conda install pytorch torchvision torchaudio pytorch-cuda=11.6 -c pytorch -c nvidia
pip install -r requirements.txt

cd demo
python demo_Laplace.py --boundary Dirichlet --dim 3
python demo_Helmholtz.py --boundary Neumann --k 3 --dim 3 --object stanford_bunny
python demo_Helmholtz_Transmission.py --boundary Full --k 5 --dim 3

Parameters

• boundary := [‘Dirichlet’, 'Neumann', 'Mix', 'Full']
  • Dirichlet: If You want to set Dirichlet boundary and solve Neumann charges, pick this.
  • Neumann: If You want to set Neumann boundary and solve Dirichlet charges, pick this.
  • Mix: If You want to set Dirichlet boundary and solve Neumann charges for y > 0, and otherwise for y <= 0, pick this. If you want to self define your design of Dirichlet region and Neumann region, go to file mesh_manager.py and reach function set_mixed_bvp, you might handle it with your own preference.
  • Full: This is only useful for Transmission problem, Both Neumann/Dirichlet boundary will be applied, and the corresponding boundary will be solved for interior.
• scope := ['Interior', 'Exterior']
  • Interior: Solve Interior problem, not applicable for transmission problem
  • Exterior: Solve Exterior problem, not applicable for transmission problem
• kernel := ['Laplace', 'Helmholtz']
  • Laplace: Solve Laplace equation
  • Helmholtz: Solve Helmholtz equation
• object := ['sphere', 'cube']
  • sphere: an obj file will be read into our scope by sphere.obj
  • You can add your own .obj files into /assets directory and use the obj file name as your own mesh object
• show_wireframe := [True, False]
  • This parameter defines if wireframe is shown in final GUI

Trouble Shooting