We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional prob...

1 A computationally efficient preconditioned conjugate gradient algorithm with a symmetric suc2 cessive over-relaxation (SSOR) preconditioner for the iterative solution of set mixed model 3 equations is described. Potential computational saving of this approach are examined for an 4 example of single-step genomic evaluation of Australian sheep. Results show that the SSOR 5 preconditioner can su...

We consider the k-Directed Steiner Forest (k-DSF) problem: given a directed graph G = (V,E) with edge costs, a collection D ⊆ V × V of ordered node pairs, and an integer k ≤ |D|, find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are...

Departing from Mulder's semi-coarsening technique for rst-order PDEs, the notion of a grid of grids is introduced and a multi-level nite-volume technique for second order elliptic PDEs is developed. Various grid-transfer operators are investigated, in combination with damped Jacobi-relaxation. Convergence rates as they are predicted by Fourier local mode analysis are compared with practical mea...

We consider the unsplittable flow problem (UFP) and the closely related column-restricted packing integer programs (CPIPs). In UFP we are given an edge-capacitated graph G = (V,E) and k request pairs R1, . . . , Rk where each Ri consists of a source-destination pair (si, ti), a demand di and a weight wi. The goal is to find a maximum weight subset of requests that can be routed unsplittably in ...

We apply a Runge-Kutta-based waveform relaxation method to initial-value problems for implicit differential equations. In the implementation of such methods, a sequence of nonlinear systems has to be solved iteratively in each step of the integration process. The size of these systems increases linearly with the number of stages of the underlying Runge-Kutta method, resulting in high linear alg...

The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value decompositions – a task that is increasingly costly as matrix sizes and ranks increase. To improve the capacity of solving large-scale problems, we propose a low-rank factorizat...

We present the results in embedding a multigrid solver for Poisson's equation into the parallel 3D Monte Carlo device simulator, PMC-3D. First we have implemented the sequential multigrid solver, and embedded it into the Monte Carlo code which previously was using the sequential successive overrelaxation (SOR) solver. Depending on the convergence threshold, we have obtained signi cant speedups ...

We utilize a nonlinear, dynamic finite element model coupled with a finite deformation viscoelastic constitutive law to study the inhomogeneous deformation and instabilities resulting from the application of a constant voltage to dielectric elastomers. The constant voltage loading is used to study electrostatically driven creep and the resulting electromechanical instabilities for two different...

the block size must be O(1= p) can be found in 2]. The observation that the overlap must be O(1= p) was also communicated to the authors by Brandt. To the best of the authors' knowledge, this paper contains the rst published numerical results and analysis. REFERENCES 1] A. Brandt. Multi{level adaptive solutions to boundary{value problems. 9 The results of this analysis agree with Observation 2....