# AMG Strategies for PDE Systems with Applications in Industrial Semiconductor Simulation

@inproceedings{Clees2005AMGSF, title={AMG Strategies for PDE Systems with Applications in Industrial Semiconductor Simulation}, author={Tanja Clees}, year={2005} }

The numerical solution of strongly coupled systems of partial differential equations (PDE systems) is commonplace in many simulation codes. Typically, large sparse matrix equations arise in the corresponding simulation runs. A serious bottleneck in performing realistic, largescale simulations is the speed by which these matrix equations can be solved. If they exceed a certain size, they can no longer be solved efficiently with standard numerical solvers, simply because these solvers are not… Expand

#### Figures, Tables, and Topics from this paper

figure 2.2 figure 2.3 figure 3.1 table 3.1 figure 3.2 table 3.2 figure 3.3 table 3.3 figure 3.4 figure 3.5 figure 3.6 figure 3.7 figure 3.8 figure 3.9 figure 4.1 table 4.1 figure 4.2 table 4.2 figure 4.3 table 4.3 figure 4.4 table 4.4 figure 4.5 table 4.5 figure 4.6 figure 4.7 figure 5.1 table 5.1 figure 5.10 table 5.10 figure 5.11 table 5.11 figure 5.12 table 5.12 figure 5.13 figure 5.14 figure 5.15 figure 5.17 figure 5.18 figure 5.19 figure 5.2 table 5.2 figure 5.20 figure 5.21 table 5.3 figure 5.3 table 5.4 figure 5.4 table 5.5 figure 5.5 table 5.6 figure 5.6 figure 5.7 table 5.7 figure 5.8 table 5.8 figure 5.9 table 5.9

#### 55 Citations

Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

- Computer Science
- 2007

This work discusses strategies for solving the fully implicit systems that preserve (or generate) the desired ellipticity property required by AMG methods and introduces an iterative coupling scheme as an alternative to fully implicit formulations that is faster and also amenable for AMG implementations. Expand

Nonsymmetric Algebraic Multigrid Based on Local Approximate Ideal Restriction (ℓAIR)

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2018

Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of… Expand

An Efficient Algebraic Multigrid Solver Strategy for Adaptive Implicit Methods in Oil Reservoir Simulation

- Computer Science
- 2007

To achieve a good compromise of high efficiency and robustness for a variety of problem classes – ranging from simple, small black-oil to challenging, large compositional models – an automatic, adaptive ILUT parameter and AMG solver switching strategy, α-SAMG, has been developed. Expand

Algebraic Multigrid (AMG) for Saddle Point Systems

- Mathematics
- 2013

We introduce an algebraic multigrid method for the solution of matrices with saddle point structure. Such matrices e.g. arise after discretization of a second order partial differential equation… Expand

Algebraic Multigrid for Stokes Equations

- Computer Science, Mathematics
- SIAM J. Sci. Comput.
- 2017

An investigation of the properties of the coarse grid matrices reveals that plain aggregation has to be preferred to maintain nice two-grid convergence at coarser levels. Expand

Application of single-level, pointwise algebraic, and smoothed aggregation multigrid methods to direct numerical simulations of incompressible turbulent flows

- Mathematics
- 2007

Single- and multi-level iterative methods for sparse linear systems are applied to unsteady flow simulations via implementation into a direct numerical simulation solver for incompressible turbulent… Expand

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

- Mathematics, Computer Science
- J. Comput. Phys.
- 2009

The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. Expand

Parallelisation of selective algebraic multigrid for block-pressure-velocity system in OpenFOAM

- Computer Science
- Comput. Phys. Commun.
- 2021

A parallel selection algebraic multigrid algorithm (AMG) based on the domain decomposition method is presented, applied for the solution of the linearised implicitly coupled pressure–velocity system discretised by the finite volume method, implemented in OpenFOAM. Expand

Improving algebraic multigrid interpolation operators for linear elasticity problems

- Mathematics, Computer Science
- Numer. Linear Algebra Appl.
- 2010

Two new methods for extending any initial AMG interpolation operator to exactly fit the rigid body modes of linear elasticity based on the introduction of additional coarse degrees of freedom at each node are proposed. Expand

Efficient algebraic multigrid for migration-diffusion-convection-reaction systems arising in electrochemical simulations

- Mathematics, Computer Science
- J. Comput. Phys.
- 2010

The article discusses components and performance of an algebraic multigrid (AMG) preconditioner for the fully coupled multi-ion transport and reaction model (MITReM) with nonlinear boundary… Expand

#### References

SHOWING 1-10 OF 123 REFERENCES

Parallel algebraic multigrid based on subdomain blocking

- Computer Science
- Parallel Comput.
- 2001

A classical AMG variant which has turned out be highly robust and efficient in solving large systems of equations corresponding to elliptic PDEs, discretized by finite differences or finite volumes is considered. Expand

A review of algebraic multigrid

- 2001

Since the early 1990s, there has been a strongly increasing demand for more e,cient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes,… Expand

Robustness of coupled Algebraic Multigrid for the Navier-Stokes equations

- Computer Science
- 1996

The feasibility of using Algebraic Multigrid as the linear equation solver for an implicit CFD method that must handle diverse applications is shown. Expand

Algebraic Multigrid for Industrial Semiconductor Device Simulation

- Computer Science
- 2003

A general framework for so-called point-based approaches is outlined and it is shown that this framework allows to construct robust and fast algebraic multigrid approaches even for cases, where iterative one-level solvers of the type commonly used in such applications exhibit bad convergence or even fail. Expand

Algebraic multigrid methods based on element preconditioning

- Mathematics, Computer Science
- Int. J. Comput. Math.
- 2001

A new algebraic multigrid solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic partial differential equation is presented. Expand

Algebraic Multigrid for Selected PDE Systems

- Computer Science
- 2002

A general framework for so-called point-based strategies for solving systems of partial differential equations by algebraic multigrid is introduced and it is shown that this framework allows to construct robust and fast algebraicMultigrid approaches even for cases, where iterative solvers of the type commonly used in such applications exhibit bad convergence or even fail. Expand

Application of an Algebraic Multigrid Solver to Process Simulation Problems

- 2003

In this paper the performance of a special algebraic multigrid (AMG) solver for the solution of the stress analysis problems in process simulation has been investigated. The discrete stress analysis… Expand

An Algebraic Multigrid Method for Linear Elasticity

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2003

An algebraic multigrid (AMG) method for the efficient solution of linear block-systems stemming from a discretization of a system of partial differential equations (PDEs) is presented and it is shown that the method provides fast convergence for a large variety of discretized elasticity problems. Expand

Algebraic Multigrid ( AMG ) for Ground Water Flow and Oil Reservoir Simulation

- 2003

A serious bottleneck in performing large-scale numerical simulations is the speed with which the underlying sparse systems of equations can be solved. If these systems exceed a certain size, they can… Expand

Application of an algebraic multigrid solver to process simulation problems

- Computer Science
- 2000 International Conference on Simulation Semiconductor Processes and Devices (Cat. No.00TH8502)
- 2000

It is shown that approaches using the AMG solver as a preconditioner are better than standard iterative solvers with regard to computing times and convergence behavior. Expand