MOOSE: A parallel computational framework for coupled systems of nonlinear equations

TLDR: MOOSE as mentioned in this paper is a parallel computational framework targeted at solving coupled, nonlinear partial di?erential equations often arise in sim- ulation of nuclear processes, which is based on mathematics based on Jacobian-free Newton Krylov (JFNK).

About: This article is published in Nuclear Engineering and Design.The article was published on 2009-10-01 and is currently open access. It has received 741 citations till now. The article focuses on the topics: Multiphysics.

Figures

Figure 4. Pebble Bed With 3 Heating Elements

Figure 3. Transient Power-up With Crack

Figure 1. MOOSE Structure

Figure 5. 3D Sodium Cooled Fast Reactor Neutron Diffion

Figure 6. 2D Sodium Cooled Fast Reactor Neutron Diffusion With h-Adaptivity

Figure 2. Convergence for Preconditioning Schemes. “Diagonal” utilizes only the diagonal blocks of M. “L+D” is lower block diagonal. “Two Sweeps” corresponds to two block Guass-Seidel iterations on (13)

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Moose: a parallel computational framework for coupled systems of nonlinear equations" ?

MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at solving these systems, is presented. 

Q2. What is the physics of a reactor?

It couples highly nonlinear mechanics, heat conduction and species diffusion equations to model fuel behavior in steady state, power-up and operational timeframes. 

Q3. What is the main preconditioning scheme used by MOOSE?

Three main preconditioning schemes are usually employed by applications: operator split using only block diagonals, lower block triangular using one block Gauss-Seidel like iteration and variable block structure utilizing multiple block Gauss-Seidel iterations. 

Q4. What is the preconditioning scheme for a two variable (g,h) system?

Forming a fully decoupled M for a two variable (g,h) system amounts to,F(g, h) = [ F1 F2 ] , (8)J ≈ M = [(F1)g 0 0 (F2)h] , (9)where (F1)g and (F2)h can be approximations and linearizations. 

Q5. What is the preconditioning technique for a block?

In particular, if the diagonal block contains a large elliptic component then multigrid preconditioning can be very effective [9]. 

Q6. How can BISON perform simulations in 2D and 3D?

After four months of development BISON can perform simulations in both 2 and 3D and on massively parallel computer architectures. 

Q7. What is the way to solve the block rows?

In the first iteration the blocks above the diagonal will be ignored, while in subsequent iterations they will be used just as the lower diagonal blocks are. 

Q8. What is the way to solve the system?

In this particular example the diagonal blocks are all elliptic dominated therefore a multigrid solver can be used to efficiently invert the systems. 

Q9. What is the preconditioner for a one-way coupled system?

Off-diagonal blocks in the lower block triangular region carry information about the coupling, allowing for a much more accurate preconditioner. 

Q10. How long has PRONGHORN been working on this?

After three months of developmentPRONGHORN is reproducing results from the SANA experiments utilizing heating rods in a bed of pebbles [11]. 

Q11. What is the way to solve the displacement rows?

In the above thermo-mechanical system changing the solve order for the displacement rows can cause up to double the number of linear iterations. 

Q12. What is the purpose of this article?

the U.S. Government2009 International Conference on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, NY, 20099/10retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. 

Q13. What is the preconditioning scheme for a block?

2009 International Conference on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, NY, 20095/10A more complex option allows for a completely variable block structure. 

Q14. What is the purpose of the paper?

MOOSE combines these ideas into a modern, general, comprehensive framework enabling rapid prototyping as well as yielding production ready massively parallel codes in a fraction of the time previously thought necessary. 

Q15. What is the preconditioning solution for a block?

Extending this idea by supplying off-diagonal blocks such that M is lower block triangular; a set of augmented systems can be solved,M = [ (F1)g 0 (F2)g (F2)h ] , (10)(F1)gq1 = v1, (11) (F2)hq2 = v2 − (F2)gq1, (12)This formulation is well suited for preconditioning one-way coupled systems.