We consider the class of the Orthogonal Projection Methods (OPM) to solve iteratively large and generalised eigenvalue problems. An OPM is a method that projects a large eigenvalue problem on a smaller subspace. In this subspace, an approximation of the eigenvalue spectrum can be computed from a small eigenvalue problem using a direct method. We show that many iterative eigenvalue solvers, such...

1. Abstract An efficient damping layout optimization method of structural-acoustic systems is proposed to minimize acoustic responses using a gradient-based optimization algorithm. To analyze vibro-acoustic systems, a hybrid model that uses finite elements for the structures and boundary element for the cavity is developed. The four-parameter fractional derivative model is used to represent the...

The scope of this study is to determine the conditions for onset instability in a horizontal porous layer subject isoflux boundary and with an infinitely wide single–cell basic flow. When circulation cellular flow absent, one recovers usual Darcy–Bénard conduction state. governing parameters are Rayleigh number associated uniform wall heat flux, dimensionless temperature gradient. latter parame...

To explore band structures of three-dimensional photonic crystals numerically, we need to solve the eigenvalue problems derived from the governing Maxwell equations. The solutions of these eigenvalue problems cannot be computed effectively unless a suitable combination of eigenvalue solver and preconditioner is chosen. Taking eigenvalue problems due to Yee’s scheme as examples, we propose using...

We analyze the Ritz–Galerkin method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates. For a simple eigenvalue, we prove an error estimate that depends mainly on the approximability of the corresponding eigenfunction and provide explicit values for all constants. For a multiple eigenvalue we prove, in addition, apparently the first truly a priori error estimates th...

Recently, we gave a theoretical explanation for superlinear convergence behavior observed while solving large symmetric systems of equations using the Conjugate Gradient method. Roughly speaking, one may observe superlinear convergence while solving a sequence of (symmetric positive definite) linear systems if the asymptotic eigenvalue distribution of the sequence of the corresponding matrices ...

In this overview we discuss iterative methods for solving large linear systems with sparse (or, possibly, structured) nonsymmetric (or, non-Hermitian) matrix that are based on the Lanczos process. They feature short recurrences for the generation of the Krylov space and for the sequence of approximations to the solution. This means low cost and low memory requirement. For very large sparse non-...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

In this work, we study the problem of onset of thermal convection in a fluid layer overlying a porous layer, the whole system being heated from below. We use Brinkman's model to describe the porous medium and determine the corresponding linear stability equations. The eigenvalue problem is solved by means of a modified Galerkin method. The behavior of the critical wave number and temperature gr...

In this paper, we present a new proof of the upper and lower bound estimates for the first Dirichlet eigenvalue λ1 (B (p, r)) of Laplacian operator for the manifold with Ricci curvature Rc ≥ −K, by using Li-Yau’s gradient estimate for the heat equation.