![7/22/2019 11
The Quasi-Minimal Residual (QMR) Solver
• The QMR solver is used for electromagnetic analyses and is available only for full
harmonic analyses [HROPT,FULL].
• (You specify the analysis type using the ANTYPE command.) You use this solver for
symmetric, complex, definite, and indefinite matrices.
• The QMR solver is more robust than the ICCG solver](https://image.slidesharecdn.com/11-typesofsolvers-190722062200/85/11-types-of-solvers-11-320.jpg)
11 types of solvers
- 1. Mechanical Solvers and their Settings
- 2. 7/22/2019 2 Types of Solvers 1. The Sparse Direct Solver 2. Distributed Sparse Direct Solver 3. The Preconditioned Conjugate Gradient (PCG) Solver 4. The Jacobi Conjugate Gradient (JCG) Solver 5. The Incomplete Cholesky Conjugate Gradient (ICCG) Solver 6. The Quasi-Minimal Residual (QMR) Solver
- 3. 7/22/2019 3 The Sparse Direct Solver • The sparse direct solver (including the Block Lanczos method for modal and buckling analyses) is based on a direct elimination of equations, as opposed to iterative solvers, where the solution is obtained through an iterative process that successively refines an initial guess to a solution that is within an acceptable tolerance of the exact solution. • Direct elimination requires the factorization of an initial very sparse linear system of equations into a lower triangular matrix followed by forward and backward substitution using this triangular system. • The space required for the lower triangular matrix factors is typically much more than the initial assembled sparse matrix, hence the large disk or in-core memory requirements for direct methods.
- 4. 7/22/2019 4 • Sparse direct solvers seek to minimize the cost of factorizing the matrix as well as the size of the factor using sophisticated equation reordering strategies. • Iterative solvers do not require a matrix factorization and typically iterate towards the solution using a series of very sparse matrix-vector multiplications along with a preconditioning step, both of which require less memory and time per iteration than direct factorization. • However, convergence of iterative methods is not guaranteed and the number of iterations required to reach an acceptable solution may be so large that direct methods are faster in some cases
- 5. 7/22/2019 5 • Because the sparse direct solver is based on direct elimination, poorly conditioned matrices do not pose any difficulty in producing a solution (although accuracy may be compromised). • Direct factorization methods always give an answer if the equation system is not singular. • When the system is close to singular, the solver can usually give a solution (although you must verify the accuracy). • The sparse solver can run completely in memory (also known as in-core) if sufficient memory is available. The sparse solver can also run efficiently by using a balance of memory and disk usage (also known as out- of-core). • The out-of-core mode typically requires about the same memory usage as the PCG solver (~1 GB per million DOFs) and requires a large disk file to store the factorized matrix (~10 GB per million DOFs). • The amount of I/O required for a typical static analysis is three times the size of the matrix factorization. • Running the solver factorization in-core (completely in memory) for modal/buckling runs can save significant amounts of wall (elapsed) time because modal/buckling analyses require several factorizations (typically 2 - 4) and repeated forward/backward substitutions (10 - 40+ block solves are typical). • The same effect can often be seen with nonlinear or transient runs which also have repeated factor/solve step
- 6. 7/22/2019 6 Distributed Sparse Direct Solver • The distributed sparse direct solver decomposes a large sparse matrix into smaller submatrices (instead of decomposing element domains), and then sends these submatrices to multiple cores on either shared-memory (e.g., server) or distributed-memory (e.g., cluster) hardware. To use more than two cores with this solver, you must have additional HPC licenses for each core beyond the first two • During the matrix factorization phase, each distributed process factorizes its submatrices simultaneously and communicates the information as necessary. • The submatrices are automatically split into pieces (or fronts) by the solver during the factorization step. The non-distributed sparse solver works on one front at a time, while the distributed sparse solver works on n fronts at the same time (where n is the total number of processes used)
- 7. 7/22/2019 7 • Each front in the distributed sparse solver is stored in-core by each process while it is factored, even while the distributed sparse solver is running in out-of-core mode. • This is essentially equivalent to the out-of-core mode for the non-distributed sparse solver. • Therefore, the total memory usage of the distributed sparse solver when using the out- of-core memory mode is about n times the memory that is needed to hold the largest front. In other words, as more cores are used the total memory used by the solver (summed across all processes) actually increases when running in this memory mode
- 8. 7/22/2019 8 • The PCG solver starts with element matrix formulation. Instead of factoring the global matrix, the PCG solver assembles the full global stiffness matrix and calculates the DOF solution by iterating to convergence (starting with an initial guess solution for all DOFs). • The PCG solver uses a proprietary pre-conditioner that is material property and element-dependent. • The PCG solver is usually about 4 to 10 times faster than the JCG solver for structural solid elements and about 10 times faster then JCG for shell elements. Savings increase with the problem size. • The PCG solver usually requires approximately twice as much memory as the JCG solver because it retains two matrices in memory: -The pre-conditioner, which is almost the same size as the stiffness matrix -The symmetric, nonzero part of the stiffness matrix The Preconditioned Conjugate Gradient (PCG) Solver
- 9. 7/22/2019 9 The Jacobi Conjugate Gradient (JCG) Solver • The JCG solver also starts with element matrix formulation. Instead of factoring the global matrix, the JCG solver assembles the full global stiffness matrix and calculates the DOF solution by iterating to convergence (starting with an initial guess solution for all DOFs). • The JCG solver uses the diagonal of the stiffness matrix as a pre-conditioner. The JCG solver is typically used for thermal analyses and is best suited for 3-D scalar field analyses that involve large, sparse matrices. • With all iterative solvers, be particularly careful to check that the model is appropriately constrained. No minimum pivot is calculated and the solver continues to iterate if any rigid body motion is possible.
- 10. 7/22/2019 10 The Incomplete Cholesky Conjugate Gradient (ICCG) Solver • The ICCG solver operates similarly to the JCG solver with the following exceptions: • The ICCG solver is more robust than the JCG solver for matrices that are not well- conditioned. Performance varies with matrix conditioning, but in general ICCG performance compares to that of the JCG solver. • The ICCG solver uses a more sophisticated pre-conditioner than the JCG solver. Therefore, the ICCG solver requires approximately twice as much memory as the JCG solver.
- 11. 7/22/2019 11 The Quasi-Minimal Residual (QMR) Solver • The QMR solver is used for electromagnetic analyses and is available only for full harmonic analyses [HROPT,FULL]. • (You specify the analysis type using the ANTYPE command.) You use this solver for symmetric, complex, definite, and indefinite matrices. • The QMR solver is more robust than the ICCG solver
- 12. 7/22/2019 12 Selecting a Solver Shared memory solver selection guidelines
- 13. 7/22/2019 13 Distributed memory solver selection guidelines
- 14. 7/22/2019 14 Some common operations are aliased to simple TUI(text user interface) commands: • ls Lists the files in the working directory • rcd Reads case and data files • wcd Writes case and data files • rc/wc Reads/writes case file • rd/wd Reads/writes data file • it Iterate
- 15. For 2D Solver • Left button translates/pans (dolly) • Middle button zooms • Right button selects/probes For 3D Solver • Left button rotates about 2 axes • Middle button zooms • Middle click on point in screen centers point in window • Right button selects/probes Mouse button functionality depends on the chosen solver (2D / 3D) and can be configured in the solver Default settings of Mouse
- 16. 7/22/2019 16 Reading the Mesh – Components • Components are defined in the preprocessor and stored in the mesh file. • Cell – The control volumes into which the domain is discretized. • Computational domain is defined by mesh that represents the fluid and solid regions of interest. • Face – The boundaries of cells • Edge – Boundary of a face • Node – Edge intersection / grid point • Zone – Grouping of nodes, faces, and/or cells. • Boundary data is assigned to face zones. • Material data and source terms are assigned to cell zones.
- 17. 7/22/2019 17 Other steps • Scaling the Mesh and Selecting Units : Any “mixed” units system can be used if desired. By default, FLUENT uses the SI system of units (specifically, MKS system). • Reordering and Modifying the Grid : The grid can be reordered so that neighboring cells are near each other in the zones and in memory. The face/cell zones can also be modified by the following operations in the Grid menu: Separation and merge of zones Fusing of cell zones with merge of duplicate faces and nodes Translate, rotate, reflect face or cell zones Extrusion of face zones to extend the domain Replace a cell zone with another or delete it Activate and Deactivate cell zones
- 18. 7/22/2019 18 • Polyhedral Mesh Conversion (if required but not mandatory) • Profile Data and Solution Data Interpolation :Profile files are data files which contain point data for selected variables on particular face zones, and can be both written and read in a FLUENT session. Similarly, Interpolation data files contain discrete data for selected field variables on particular cell zones to be written and read into FLUENT.