Multilevel preconditioners for simulations and optimization on dynamic, adaptive meshes
نویسندگان
چکیده
We present adaptive preconditioners for parallel, time-dependent simulations and nonlinear optimization problems with dynamic mesh adaptation. Adaptive meshing greatly reduces the computational cost of simulations and optimization. Unfortunately, it also carries a number of problems for preconditioning in iterative linear solvers, as changes in the mesh lead to structural changes in the linear systems we must solve. As a result, a new preconditioner must be computed after every change in the mesh, which might be prohibitively expensive. Here, we propose preconditioners that are cheap to update for dynamic changes to the mesh as well as for changes in the matrix due to nonlinearity of the underlying problem; more specifically, we propose preconditioners that require only local changes to the preconditioner for local changes in the mesh and nonlinear terms. Our preconditioners combine sparse approximate inverses with multilevel correction [1] and [2].
منابع مشابه
Multilevel Sparse Approximate Inverse Preconditioners for Adaptive Mesh Refinement∗
We present an efficient and effective preconditioning method for time-dependent simulations with dynamic, adaptive mesh refinement and implicit time integration. Adaptive mesh refinement greatly improves the efficiency of simulations where the solution develops steep gradients in small regions of the computational domain that change over time. Unfortunately, adaptive mesh refinement also introd...
متن کاملA Framework for Parallel Adaptive
Finite element meshes are large, richly structured sets whose internal relationships must be visible to diierent parts of a nite element program. This causes software engineerings problems that increase when adaptive mesh reenement and multilevel preconditioners are applied. Even more problems arise when nite element methods have to be implemented for parallel computers since the meshes have to...
متن کاملLocal Refinement and Multilevel Preconditioning: Implementation and Numerical Experiments
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinementbased discretizations of elliptic equations, they tend to be less effective for algebraic systems which arise from discretizations on locally refined meshe...
متن کاملParallel Multilevel Preconditioners
In this paper, we provide techniques for the development and analysis of parallel multilevel preconditioners for the discrete systems which arise in numerical approximation of symmetric elliptic boundary value problems. These preconditioners are defined as a sum of independent operators on a sequence of nested subspaces of the full approximation space. On a parallel computer, the evaluation of ...
متن کاملMultilevel Solvers for Unstructured Surface Meshes
Parameterization of unstructured surface meshes is of fundamental importance in many applications of Digital Geometry Processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, suc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009