Assertion checking of control dominated systems with nonlinear solvers

2006 ◽  
Author(s):  
I. Ugarte ◽  
P. Sanchez
Keyword(s):  
Nonlinear Solvers

scholarly journals PyTrilinos: Recent Advances in the Python Interface to Trilinos

2012 ◽  
Vol 20 (3) ◽  
pp. 311-325 ◽  
Author(s):  
William F. Spotz
Keyword(s):  
Linear Algebra ◽  
Utility Functions ◽  
Ease Of Use ◽  
Linear Solution ◽  
Dense Linear Algebra ◽  
Multilevel Preconditioners ◽  
Front End ◽  
Nonlinear Solvers ◽  
Sparse Linear Algebra ◽  
Python Package

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of the underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.

scholarly journals Computation of Nonlinear Thermoelectric Effects with Adaptive Methods

2020 ◽  
Vol 76 (3) ◽  
pp. 75-84
Author(s):  
Aizuddin Mohamed ◽  
Razi Abdul-Rahman
Keyword(s):  
Fixed Point ◽  
Electric Potential ◽  
Computing Time ◽  
Three Dimensions ◽  
Adaptive Finite Element Method ◽  
Tetrahedral Mesh ◽  
Posteriori Error Estimate ◽  
Nonlinear Solution ◽  
Nonlinear Solvers ◽  
Anderson Acceleration

An implementation for a fully automatic adaptive finite element method (AFEM) for computation of nonlinear thermoelectric problems in three dimensions is presented. Adaptivity of the nonlinear solvers is based on the well-established hp-adaptivity where the mesh refinement and the polynomial order of elements are methodically controlled to reduce the discretization errors of the coupled field variables temperature and electric potential. A single mesh is used for both fields and the nonlinear coupling of temperature and electric potential is accounted in the computation of a posteriori error estimate where the residuals are computed element-wise. Mesh refinements are implemented for tetrahedral mesh such that conformity of elements with neighboring elements is preserved. Multiple nonlinear solution steps are assessed including variations of the fixed-point method with Anderson acceleration algorithms. The Barzilai-Borwein algorithm to optimize the nonlinear solution steps are also assessed. Promising results have been observed where all the nonlinear methods show the same accuracy with the tendency of approaching convergence with more elements refining. Anderson acceleration is the most efficient among the nonlinear solvers studied where its total computing time is less than half of the more conventional fixed-point iteration.

scholarly journals A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling*

2021 ◽  
Vol 253 (2) ◽  
pp. 52
Author(s):  
M. Paul Laiu ◽  
Eirik Endeve ◽  
Ran Chu ◽  
J. Austin Harris ◽  
O. E. Bronson Messer
Keyword(s):  
Matter Coupling ◽  
Nonlinear Solvers

Trilinos Solvers Scalability on a MFiX-Trilinos Framework Applied to Fluidized Bed Simulations

2020 ◽  
Author(s):  
Arturo Rodriguez ◽  
V. M. Krushnarao Kotteda ◽  
Luis F. Rodriguez ◽  
Vinod Kumar ◽  
Jorge A. Munoz
Keyword(s):  
Linear System ◽  
Fluidized Bed ◽  
Large Scale ◽  
Fossil Fuel ◽  
State Of The Art ◽  
Iterative Solvers ◽  
Flow Solver ◽  
Nonlinear Solvers ◽  
Fuel Reactor ◽  
Preconditioned Iterative

Abstract MFiX is a multiphase open-source suite that is developed at the National Energy Technology Laboratories. It is widely used by fossil fuel reactor communities to simulate flow in a fluidized bed reactor. It does not have advanced linear iterative solvers even though it spends 70% of the run time in solving the linear system. Trilinos contains algorithms and enabling technologies for the solution of large-scale, sophisticated multi-physics engineering and scientific problems. The library developed at Sandia National Laboratories has more than 60 packages. It consists of state-of-the-art preconditioners, nonlinear solvers, direct solvers, and iterative solvers. The packages are performant and portable on various hybrid computing architectures. To improve the capabilities of MFiX, we developed a framework, MFiX-Trilinos, to integrate the advanced linear solvers in Trilinos with the FORTRAN based multiphase flow solver, MFiX. The framework changes the semantics of the array in FORTRAN and C++ and solve the linear system with packages in Trilinos and returns the solution to MFiX. The preconditioned iterative solvers considered for the analysis are BiCGStab and GMRES. The framework is verified on various fluidized bed problems. The performance of the framework is tested on the Stampede supercomputer. The wall time for multiple sizes of fluidized beds is compared.

An Adaptive Sequential Fully Implicit Domain-Decomposition Solver

SPE Journal ◽  
2021 ◽  
pp. 1-13
Author(s):  
Ø. S. Klemetsdal ◽  
A. Moncorgé ◽  
H. M. Nilsen ◽  
O. Møyner ◽  
K-. A. Lie
Keyword(s):  
Domain Decomposition ◽  
Reservoir Simulation ◽  
Rock Properties ◽  
Solution Strategy ◽  
Flow And Transport ◽  
Solution Strategies ◽  
Fully Implicit ◽  
Fluid Behavior ◽  
Nonlinear Solver ◽  
Nonlinear Solvers

Summary Modern reservoir simulation must handle complex compositional fluid behavior, orders-of-magnitude variations in rock properties, and large velocity contrasts. We investigate how one can use nonlinear domain-decomposition preconditioning to combine sequential and fully implicit (FI) solution strategies to devise robust and highly efficient nonlinear solvers. A full simulation model can be split into smaller subdomains that each can be solved independently, treating variables in all other subdomains as fixed. In subdomains with weaker coupling between flow and transport, we use a sequential fully implicit (SFI) solution strategy, whereas regions with stronger coupling are solved with an FI method. Convergence to the FI solution is ensured by a global update that efficiently resolves long-range interactions across subdomains. The result is a solution strategy that combines the efficiency of SFI and its ability to use specialized solvers for flow and transport with the robustness and correctness of FI. We demonstrate the efficacy of the proposed method through a range of test cases, including both contrived setups to test nonlinear solver performance and realistic field models with complex geology and fluid physics. For each case, we compare the results with those obtained using standard FI and SFI solvers. This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

How to stabilize nonlinear solvers for rate-independent plasticity problems?

2020 ◽  
Author(s):  
Anton Popov ◽  
Georg Reuber
Keyword(s):  
Jacobian Matrix ◽  
Physical Phenomenon ◽  
Localization Length ◽  
Iterative Algorithms ◽  
Limiting Factor ◽  
Direct Solver ◽  
Rate Dependent ◽  
Nonlinear Solvers ◽  
Equivalent Rate ◽  
The Difference

<p>Plastic strain localization in a rate-independent limit is a physical phenomenon that demands robust and reliable nonlinear solves to be modeled in a computer. It is quite common on practice that standard iterative algorithms (e.g. Newton-Raphson), being applied to this demanding problem, lead to  convergence issues or even fail. From the physical viewpoint the problem can be attributed to the difference between the dilatation and friction angles for the pressure-sensitive materials, which gets worse as this difference gets larger.</p><p>Common remedies include deriving consistent Jacobian matrix, or switching to the equivalent rate-dependent visco-plastic formulation. Both methods have their specific side effects. A very high condition number of a heavily unsymmetrical Jacobian matrix renders it nearly useless in the context of an iterative linear solver, such as multigrid. Hence, the use of the Jacobian matrix is essentially limited to a 2D formulation, for which a direct solver is practical. The visco-plastic formulation is confusing form the conceptual viewpoint. It strives to achieve the convergence by modifying the physics of the problem. Hence, the stabilization viscosity is not a pure numerical parameter that can be freely selected, but it is a physical parameter that must be determined in the laboratory. The advantages of the visco-plastic formulation vanish, if rate-independent limit is considered, or if affordable grid size is (much) larger than the intrinsic localization length-scale. The latter condition is a dominant limiting factor for a 3D model. </p><p>In this work we share a few recipes, that can potentially improve the convergence of the rate-independent plasticity problems, without relying on the availability of a direct solver, or perturbing the physics.</p>

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