We derive and analyze new boundary element (BE) based finite element discretizations of potential-type, Helmholtz and Maxwell equations on arbitrary polygonal and polyhedral meshes. The starting point of this discreti...
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ISBN:
(纸本)9783642026775;9783642026768
We derive and analyze new boundary element (BE) based finite element discretizations of potential-type, Helmholtz and Maxwell equations on arbitrary polygonal and polyhedral meshes. The starting point of this discretization technique is the symmetric BE Domain Decomposition Method (DDM), where the subdomains are the finite elements. This can be interpreted as a local Trefftz method that uses PDE-harmonic basis functions. This discretization technique leads to large-scale sparse linear systems of algebraic equations which can efficiently be solved by Algebraic Multigrid (AMG) methods or AMG preconditioned conjugate gradient methods in the case of the potential equation and by Krylov subspace iterative methods in general.
In this note, we extend the mathematical framework in [7] of barrier methods for state constrained optimal control problems with PDEs to a more general setting. In [7] we modelled the state equation by Ly = u with L a...
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In this paper, we present a parallel computational framework for the completely automated design of a Vertical Axis Fluid Turbine (VAFT). Simulation, Optimum design, Fabrication and Testing (SOFT) of the VAFT is integ...
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We are motivated by an optimization problem arising in computational scaling for optical lithography that reduces to finding the point of minimum radius that lies outside of the union of a set of diamonds centered at ...
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ISBN:
(纸本)9783642026775;9783642026768
We are motivated by an optimization problem arising in computational scaling for optical lithography that reduces to finding the point of minimum radius that lies outside of the union of a set of diamonds centered at the origin of Euclidean space of arbitrary dimension. A decomposition of the feasible region into convex regions suggests a heuristic sampling approach to finding the global minimum. We describe a technique for decomposing the surface of a hypersphere of arbitrary dimension, both exactly and approximately, into a specific number of regions of equal area and small diameter. The decomposition generalizes to any problem posed on a spherical domain where regularity of the decomposition is an important concern. We specifically consider a storage-optimized decomposition and analyze its performance. We also show how the decomposition can parallelize the sampling process by assigning each processor a subset of points on the hypersphere to sample. Finally, we describe a freely available C++ software package that implements the storage-optimized decomposition.
The numerical solution of very large 3D electromagnetic field problems are challenging for various applications in the industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the...
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ISBN:
(纸本)9783642026775;9783642026768
The numerical solution of very large 3D electromagnetic field problems are challenging for various applications in the industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the 3D Maxwell equations on MIMD computers, based on a mixed variational formulation. It is especially well adapted for the solution of the Vlasov-Maxwell equations, widely used to simulate complex devices like particle injectors or accelerators. This approach in particular leads to reuse without modification most of an existing sequential code.
We consider a multigrid method for solving the discretized optimality system of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a class of el...
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ISBN:
(纸本)9783642026775;9783642026768
We consider a multigrid method for solving the discretized optimality system of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a class of elliptic optimal control problems. A rigorous multigrid convergence analysis yields level-independent convergence rates. Numerical experiments indicate that the convergence rates are also independent of the involved regularization parameter.
Non-matching grids are becoming more and more common in scientific computing. Examples are the Chimera methods proposed by [20] and analyzed in [2], the mortar methods in domain decomposition by [1], and the patch met...
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In many applications one needs to solve a discrete system of linear equations with a symmetric block matrix M (u/p) ≡ (A BT/B O) (u/p) = (f/g,) where the block A =AT is not necessarily positive definite and may even ...
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In this paper, a new solution methodology based on the FETI-2LM method for non conforming grids is introduced. Thanks to the regularizing properties of the Robin interface matching conditions of the FETI-2LM method, e...
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Harmonic functions attain their pointwise maximum on the boundary of the domain. In this article, we analyze the relationship between various norms of nearly harmonic functions and we show that the trace norm is maxim...
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ISBN:
(纸本)9783642026775
Harmonic functions attain their pointwise maximum on the boundary of the domain. In this article, we analyze the relationship between various norms of nearly harmonic functions and we show that the trace norm is maximized on the boundary of the domain. One application is that the Optimized Schwarz Method with two subdomains converges for all Robin parameters alpha > 0.
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