文件列表:

BinFileGeneration/ (0, 2023-09-18)
BinFileGeneration/JKS/ (0, 2023-09-18)
BinFileGeneration/JKS/Domain.exp (1164, 2023-09-18)
BinFileGeneration/JKS/Front.exp (422, 2023-09-18)
BinFileGeneration/JKS/Jks.par (3236, 2023-09-18)
BinFileGeneration/JKS/WeakB.exp (2016, 2023-09-18)
BinFileGeneration/JKS/runme.m (1816, 2023-09-18)
BinFileGeneration/PIG/ (0, 2023-09-18)
BinFileGeneration/PIG/DomainOutline.exp (687, 2023-09-18)
BinFileGeneration/PIG/FrontRetreat.exp (508, 2023-09-18)
BinFileGeneration/PIG/Pig.par (6373, 2023-09-18)
BinFileGeneration/PIG/runme.m (3866, 2023-09-18)
LICENSE (1067, 2023-09-18)
docs/ (0, 2023-09-18)
docs/Element Size/ (0, 2023-09-18)
docs/Element Size/fig_JakobshavnIsbrae_1e6_DoFs.png (137962, 2023-09-18)
docs/Element Size/fig_JakobshavnIsbrae_2e7_DoFs.png (138721, 2023-09-18)
docs/Element Size/fig_JakobshavnIsbrae_3e5_DoFs.png (520721, 2023-09-18)
docs/Element Size/fig_JakobshavnIsbrae_7e5_DoFs.png (524613, 2023-09-18)
docs/Element Size/fig_JakobshavnIsbrae_8e4_DoFs.png (486693, 2023-09-18)
docs/Element Size/fig_PineIslandGlacier_1e5DoFs.png (330184, 2023-09-18)
docs/Element Size/fig_PineIslandGlacier_2e4DoFs.png (471739, 2023-09-18)
docs/Element Size/fig_PineIslandGlacier_2e6DoFs.png (329992, 2023-09-18)
docs/Element Size/fig_PineIslandGlacier_7e4DoFs.png (543552, 2023-09-18)
docs/fig_gmd.pdf (200961, 2023-09-18)
docs/fig_iter2convergence.pdf (39318, 2023-09-18)
docs/fig_mtpeff.pdf (15922, 2023-09-18)
docs/fig_pt_flowchart.pdf (70766, 2023-09-18)
docs/fig_walltime.pdf (18043, 2023-09-18)
output/ (0, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/ (0, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/JKS1e6.outlog (4437, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/JKS2e7.outlog (3947, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/JKS3e5.outlog (3541, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/JKS7e5.outlog (3343, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/JKS8e4.outlog (3043, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/PIG1e5.outlog (3328, 2023-09-18)
output/64-bit 18-core Intel Xeon Gold 6140 processor/PIG2e4.outlog (3339, 2023-09-18)
... ...

# FastIceFlo [](https://zenodo.org/badge/latestdoi/288527136) This study aims to provide a graphics processing unit accelerated ice flow solver for unstructured meshes using the Shallow Shelf Approximation. This repository relates to the original research article published in the **Geoscientific Model Development** journal: ``` @Article{gmd-xx, AUTHOR = {Sandip, A. and R\"ass, L. and Morlighem, M.}, TITLE = {Graphics processing unit accelerated ice flow solver for unstructured meshes using the Shallow Shelf Approximation (FastIceFlo v1.0)}, JOURNAL = {Geoscientific Model Development}, VOLUME = {xx}, YEAR = {xx}, NUMBER = {xx}, PAGES = {xx--xx}, URL = {xx}, DOI = {xx} } ``` ## 2-D Shallow shelf approximation (SSA) We employ SSA to solve the momentum balance to predict ice-sheet flow: $\nabla \cdot \left(2 H \mu \dot{\boldsymbol{\varepsilon}} \right) = \rho g H\nabla s + \alpha^2 {\bf v}$ , where $H$ is the ice thickness distribution, $\mu$ the dynamic ice viscosity, $\dot{\boldsymbol{\varepsilon}}$ the effective strain rate, $\rho$ the ice density, $g$ the gravitational acceleration, $s$ glacier's upper surface z-coordinate and $\alpha^2 {\bf v}$ is the basal friction. As boundary conditions, we apply water pressure at the ice front $\Gamma_{\sigma}$, and non-homogeneous Dirichlet boundary conditions on the other boundaries $\Gamma_u$ (based on observed velocity). ### Pseudo-transient (PT) method We reformulate the 2-D SSA steady-state momentum balance equations to incorporate the usually ignored inertial terms: $\nabla \cdot \left(2 H \mu \dot{\boldsymbol{\varepsilon}}_{SSA} \right) -\rho g H\nabla s - \alpha^2 {\bf v} = \rho H\frac{\partial \bf v}{\partial \tau}$ , which allows us to turn the steady-state equations into transient diffusion of velocities $v_{x,y}$. The velocity-time derivatives represent physically motivated expressions we can further use to iteratively reach a steady state, thus the solution of the system. ### Weak form The weak form (assuming homogeneous Dirichlet conditions along all model boundaries for simplicity) reads: $\forall {\bf w}\in {\mathcal H}^1\left(\Omega\right)$ , $\int_\Omega {\rho} H\frac{\partial {\bf v}}{\partial \tau} \cdot {\bf w} d\Omega$ + $\int_\Omega 2 H {\mu} \dot{\boldsymbol{\varepsilon}} : \dot{\boldsymbol{\varepsilon}}_{w} d\Omega$ = $\int_\Omega - \rho g H \nabla s \cdot {\bf w} - \alpha^2 {\bf v} \cdot {\bf w} d\Omega$ where ${\mathcal H}^1\left(\Omega\right)$ is the space of square-integrable functions whose first derivatives are also square integrable. Once discretized using the finite-element method, the matrix system to solve is: $\boldsymbol{M} \dot{\bf V} + \boldsymbol{K}{\bf V} = \boldsymbol{F}$ , where $\boldsymbol{M}$ is the mass matrix, $\boldsymbol{K}$ is the stiffness matrix, $\boldsymbol{F}$ is the right hand side or load vector, and ${\bf V}$ is the vector of ice velocity. For every nonlinear PT iteration, we compute the rate of change in velocity $\dot{\bf v}$ and the explicit CFL time step $\Delta \tau$. We then deploy the reformulated 2D SSA momentum balance equations to update ice velocity $\bf v$ followed by ice viscosity $\mu_{eff}$. [We iterate in pseudo-time until the stopping criterion is met](docs/fig_pt_flowchart.pdf). ## Steps to run the code ### Step 1: Generate glacier model configurations To test the performance of the PT method beyond simple idealized geometries, we apply it to two regional-scale glaciers: [Jakobshavn Isbr, in western Greenland, and Pine IslandGlacier, in west Antarctica](docs/fig_gmd.pdf). To generate the glacier model configurations, follow the steps listed below: 1. Install [ISSM](https://issm.jpl.nasa.gov/download/) and download the datasets 2. Run `runme.m` script to generate the [Jakobshavn Isbr](BinFileGeneration/JKS/runme.m) or [Pine Island](BinFileGeneration/PIG/runme.m) Glacier models 3. Save the `.mat` file and corresponding `.bin` file ### Step 2: Hardware implementation We developed a CUDA C implementation to solve the SSA equations using the PT approach on unstructured meshes. We choose a stopping criterion of $||v^{old} - v||_{\infty}$ < 10 m $yr^{-1}$. To execute on a NVIDIA Tesla V100 GPU and view results, follow the steps listed below: 1. Clone or download this repository. 2. Transfer the `.bin` file generated along with files in [src](src) folder to a directory on a system hosting a (recent) Nvidia CUDA-capable GPU (here shown for a Tesla V100) 3. Plug in the damping parameter $\gamma$, non-linear viscosity relaxation scalar $\theta_{\mu}$ and relaxation $\theta_v$ for the chosen glacier model configuration and spatial resolution 4. Compile the [`ssa_fem_pt.cu`](src/ssa_fem_pt.cu) routine ```bash nvcc -arch=sm_70 -O3 -lineinfo ssa_fem_pt.cu -Ddmp=$damp -Dstability=$vel_rela -Drela=$visc_rela ``` 5. Run the generated executable `./a.out` 6. Along with a `.txt` file that stores the computational time, effective memory throughput and the PT iterations to meet stopping criterion, a `.outbin` file will be generated. 7. Save the `.outbin` file | Jakobshavn Isbr number of vertices | $\gamma$ | $\theta_v$ | $\theta_{\mu}$ | Block size | | :----: | :----: | :----: | :----: |:----: | | 44229 | 0.98 | 0.99 | 3e-2 | 128 | | 164681 | 0.987 | 0.98 | 7e-2 | 128 | | 393771 | 0.99 | 0.99 | 1e-1 | 1024 | | 667729 | 0.992 | 0.999 | 1e-1 | 1024 | | 10664257 | 0.998 | 0.999 | 1e-1 | 1024 | | Pine Island Glacier number of vertices | $\gamma$ | $\theta_v$ | $\theta_{\mu}$ |Block size | | :----: | :----: | :----: | :----: |:----: | | 14460 | 0.98 | 0.6 | 1e-1 | 128 | | 35646 | 0.99 | 0.49 | 8e-2 | 256 | | 69789 | 0.991 | 0.99 | 2e-2 | 512 | | 1110705 | 0.998 | 0.995 | 1e-2 | 1024 | Table 1. Optimal combination of damping parameter $\gamma$, non-linear viscosity relaxation scalar $\theta_{\mu}$ and relaxation $\theta_v$ to maintain the linear scaling and solution stability for the glacier model configurations and DoFs listed. Optimal block size was chosen to minimize wall time. ### Step 3: Post-processing To extract and plot the ice velocity distribution, follow the steps listed below: 1. Transfer `.mat` file and the `.outbin` files generated from steps 1 and 2 to a directory in MATLAB 2. Activate the ISSM environment 3. Execute the following statements in the MATLAB command window: ```Matlab load "insert name of .mat file here" md.miscellaneous.name = 'output'; md=loadresultsfromdisk(md, 'output.outbin'); plotmodel(md,'data',sqrt(md.results.PTsolution.Vx.^2 + md.results.PTsolution.Vy.^2)); ``` 3. View results ## Questions/Comments/Discussion For questions, comments and discussions please post in the FastIceFlo discussions [discussions](https://github.com/AnjaliSandip/FastIceFlo/discussions) forum.

近期下载者：

相关文件：

评论：[我要评论] [举报此文件]

收藏者：