We consider time-dependent PDEs discretized in combined space-time domains. We first reduce the PDE to a first order system. Very often in practice, one of the equations of the reduced system involves the divergence operator (in space-time). The popular FOSLS (first order system least-squares) method is then applied modified by keeping the divergence equation as a constraint which we refer to as CFOSLS (constrained FOSLS). Applying finite elements to discretize the CFOSLS problem leads to a saddle-point system. To alleviate the high memory demand of the combined space-time approach (due to the increased dimension), we apply element agglomeration AMG upscaling on space-time elements. This leads to substantially reduced problem sizes with controlled accuracy. Initial numerical results for model parabolic and scalar hyperbolic problems illustrate the potential of the method.

Researchers should cite this work as follows:

• Panayot Vassilevski (2016), "Space-time constrained FOSLS with AMGe upscaling," https://nanohub.org/resources/23516.

  BibTex | EndNote

1. algorithms
2. AMGe
3. constrained
4. first order system least-squares (FOSLS)
5. FOSLS
6. Illinois
7. least squares
8. NanoBio Node at Illinois
9. PDEs
10. space-time
11. upscaling