Projection based variational multiscale (VMS) methods are a very successful technique in the numerical simulation of high Reynolds number flow problems using coarse discretizations. However, their implementation into ...
详细信息
ISBN:
(纸本)9783319399294;9783319399270
Projection based variational multiscale (VMS) methods are a very successful technique in the numerical simulation of high Reynolds number flow problems using coarse discretizations. However, their implementation into an existing (legacy) codes can be very challenging in practice. We propose a second order variant of projection-based VMS method for non-isothermal flow problems. The method adds stabilization as a decoupled post-processing step for both velocity and temperature, and thus can be efficiently and easily used with existing codes. In this work, we propose the algorithm and give numerical results for convergence rates tests and coarse mesh simulation of Marsigli flow.
In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subspace methods for solving complex symm...
详细信息
ISBN:
(纸本)9783319399294;9783319399270
In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subspace methods for solving complex symmetric linear systems with multiple right hand sides. The proposed Block iterative solvers can fully exploit the complex symmetry property of coefficient matrix of the linear system. We report on extensive numerical experiments to show the favourable convergence properties of our newly developed Block algorithms for solving realistic electromagnetic simulations.
In this paper we discuss the adjoint stabilised finite element method introduced in Burman (SIAM J Sci Comput 35( 6): A2752-A2780, 2013) and how it may be used for the computation of solutions to problems for which th...
详细信息
ISBN:
(纸本)9783319416403;9783319416380
In this paper we discuss the adjoint stabilised finite element method introduced in Burman (SIAM J Sci Comput 35( 6): A2752-A2780, 2013) and how it may be used for the computation of solutions to problems for which the standard stability theory given by the Lax-Milgram Lemma or the Babuska-Brezzi Theorem fails. We pay particular attention to ill-posed problems that have some conditional stability property and prove (conditional) error estimates in an abstract framework. As a model problem we consider the elliptic Cauchy problem and provide a complete numerical analysis for this case. Some numerical examples are given to illustrate the theory.
We introduce an abstract concept for decomposing spaces with respect to a substructuring of a bounded domain. In this setting we define weakly conforming finite element approximations of quadratic minimization problem...
详细信息
ISBN:
(纸本)9783319399294;9783319399270
We introduce an abstract concept for decomposing spaces with respect to a substructuring of a bounded domain. In this setting we define weakly conforming finite element approximations of quadratic minimization problems. Within a saddle point approach the reduction to symmetric positive Schur complement systems on the skeleton is analyzed. Applications include weakly conforming variants of least squares and minimal residuals.
The sparse grid combination technique provides a framework to solve high-dimensional numerical problems with standard solvers by assembling a sparse grid from many coarse and anisotropic full grids called component gr...
详细信息
ISBN:
(数字)9783319282626
ISBN:
(纸本)9783319282626;9783319282602
The sparse grid combination technique provides a framework to solve high-dimensional numerical problems with standard solvers by assembling a sparse grid from many coarse and anisotropic full grids called component grids. Hierarchization is one of the most fundamental tasks for sparse grids. It describes the transformation from the nodal basis to the hierarchical basis. In settings where the component grids have to be frequently combined and distributed in a massively parallel compute environment, hierarchization on component grids is relevant to minimize communication overhead. We present a cache-oblivious hierarchization algorithm for component grids of the combination technique. It causes vertical bar G(l)vertical bar . (1/B + O (1/(d)root M)) cache misses under the tall cache assumption M = omega (B-d).(1) Here, G(l) denotes the component grid, d the dimension, M the size of the cache and B the cache line size. This algorithm decreases the leading term of the cache misses by a factor of d compared to the unidirectional algorithm which is the common standard up to now. The new algorithm is also optimal in the sense that the leading term of the cache misses is reduced to scanning complexity, i.e., every degree of freedom has to be touched once. We also present a variant of the algorithm that causes vertical bar G(l)vertical bar . (2/B + O (1/(d-1)root ***-2)) cache misses under the assumption M = omega (B). The new algorithms have been implemented and outperform previously existing software. In several cases the measured performance is close to the best possible.
In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the ...
详细信息
ISBN:
(数字)9783319282626
ISBN:
(纸本)9783319282626;9783319282602
In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution's mean and its covariance with leading order in the amplitude of the random domain perturbation. The partial differential equation for the covariance is a tensor product Dirichlet problem which can efficiently be determined by Galerkin's method in the sparse tensor product space. We show that this Galerkin approximation coincides with the solution derived from the combination technique if the detail spaces in the related multiscale hierarchy are constructed with respect to Galerkin projections. This means that the combination technique does not impose an additional error in our construction. Numerical experiments quantify and qualify the proposed method.
暂无评论