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**Author of this lecture: [Wenxin Du](https://dwxrycb123.github.io/), University of California, Los Angeles & Shanghai Jiaotong University*
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**Author of this lecture: [Wenxin Du](https://dwxrycb123.github.io/), University of California, Los Angeles*
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To extend the IPC method to rigid body contact, we can employ subspace methods to effectively reduce the system's degrees of freedom (DOFs). Since a rigid body serves as an idealized model for extremely stiff real-world objects with negligible deformation, it does not require a large number of DOFs. This observation motivates the Affine Body Dynamics (ABD) {{#cite lan2022affine}} method. Depending on the choice of subspace, this approach can also be adapted into various algorithms suitable for different categories of soft bodies.
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## GPU-Accelerated Simulation
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**Author of this section: [Zhaofeng Luo](https://roushelfy.github.io/), Carnegie Mellon University & Peking University*
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**Author of this section: [Zhaofeng Luo](https://roushelfy.github.io/), Carnegie Mellon University*
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We now rewrite the 2D mass-spring simulator to leverage GPU acceleration.
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Instead of directly writing [CUDA](https://developer.nvidia.com/cuda-toolkit), we resort to [MUDA](https://github.com/MuGdxy/muda), a lightweight library that provides a simple interface for GPU-accelerated computations.
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