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73 lines
4.2 KiB
73 lines
4.2 KiB
2 years ago
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#### 0. 待测线性系统：规模为50w*50w，非零项nnz为1.7e7。来源：lattice晶格压缩工况的IPC仿真。
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#### 1. AMGCL：CPU backend (花费主要在solve上)
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| solver | Relaxation | Coarsening | Time cost (s) |
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| ---------- | ---------------- | ----------------------------------------------------- | ------------- |
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| CG | gauss_seidel | ruge_stuben | 51.55 |
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| CG | gauss_seidel | aggregation | 31.56 |
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| CG | gauss_seidel | smoothed_aggregation (eps_strong=0.0, block_size = 3) | 38.48 |
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| CG | gauss_seidel | smoothed_aggr_emin (eps_strong=0.0, block_size = 3) | 42.70 |
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| CG | spai0 | aggregation | 51.30 |
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| LGMRES | gauss_seidel | ruge_stuben | 25.54 |
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| **LGMRES** | **gauss_seidel** | **aggregation** | **17.86** |
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| LGMRES | gauss_seidel | smoothed_aggregation (eps_strong=0.0, block_size = 3) | 30.30 |
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| LGMRES | gauss_seidel | smoothed_aggr_emin (eps_strong=0.0, block_size = 3) | 34.64 |
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| LGMRES | spai0 | aggregation | 38.44 |
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#### 2. AMGCL：CUDA Backend (GPU: GeForce GTX 1080 Ti，花费主要在setup上)
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| solver | Relaxation | Coarsening | Time cost (s) |
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| ------------------ | ---------- | ----------------------------------------------------- | ------------- |
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| CG | spai0 | ruge_stuben | 7.35 |
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| CG | spai0 | aggregation | 4.30 |
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| CG | spai0 | smoothed_aggregation (eps_strong=0.0, block_size = 3) | 9.98 |
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| CG | spai0 | smoothed_aggr_emin (eps_strong=0.0, block_size = 3) | 14.78 |
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| BiCGStabL(L=2) | spai0 | ruge_stuben | 7.85 |
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| **BiCGStabL(L=2)** | **spai0** | **aggregation** | **3.88** |
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| BiCGStabL(L=2) | spai0 | smoothed_aggregation (eps_strong=0.0, block_size = 3) | 10.10 |
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| BiCGStabL(L=2) | spai0 | smoothed_aggr_emin (eps_strong=0.0, block_size = 3) | 15.07 |
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| LGMRES | spai0 | ruge_stuben | 7.55 |
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| LGMRES | spai0 | aggregation | 4.22 |
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| LGMRES | spai0 | smoothed_aggregation (eps_strong=0.0, block_size = 3) | 10.06 |
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| LGMRES | spai0 | smoothed_aggr_emin (eps_strong=0.0, block_size = 3) | 14.44 |
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#### 3. 该系统分别用CHOLMOD和cuSolver求解所需要的时间
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| CHOLMOD | 9.05s |
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| ------------------------------------------------------------ | ------ |
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| cuSolver (GPU: GeForce GTX 1080 Ti, solver=chol, reorder=metis) | 17.11s |
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#### 4. 关于AMGCL中backend，solver，Preconditioner，relaxation，coarsening选取的总结（仅针对该线性系统，不适合所有情况）
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##### backend：
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* CUDA比CPU (builtin)快**5-12倍**左右
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##### solver：
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* CPU上，较快：FGMRES > LGMRES > CG；BiCGStab没测；IDR(s)和Richardson较慢
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* CUDA上，CG, BiCGStab, LGMRES, FGMRES性能接近，较快；IDR(s)和Richardson较慢
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**Preconditioners：**
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* AMG较快，其他没测试，Composite preconditioner针对the solution of saddle point或者Stokes-like systems
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##### Relaxation：
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* CPU上，较快：Gauss-Seidel和SPAI0，较慢：Damped Jacobi, Chebyshev, ILU, SPAI1
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* CUDA上，较快：SPAI0，较慢：Damped Jacobi, Chebyshev, ILU, SPAI1，不能使用：Gauss-Seidel
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##### Coarsening：
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* CPU和CUDA的结论一致，aggregation > ruge_stuben > smoothed aggregation > smoothed_aggr_emin
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