We consider the linear equation Ax = b where A is a sparse symmetric positive definite matrix arising from a finite element discretisation. We use the preconditioned conjugate gradient method to solve this equation, introducing an element-by-element preconditioner which is based on a Crout's decomposition of the element matrices and an element-by-element product of them. When the mesh is colour...

This paper describes a full wave approach for analyzing planar interconnect structures, such as power distribution systems in printed circuit boards and multichip modules, using a tightly coupled combination of FDTD and SPICE. The technique enhances the present hybrid full wave circuit methods in terms of robustness and efficiency. The method is applied to a few sample problems to illustrate it...

The Hunter–Saxton equation is the Euler equation for the geodesic flow on the quotient space of the infinite-dimensional group of orientation preserving diffeomorphisms of the unit circle modulo the subgroup of rigid rotations equipped with a right-invariant metric. We establish several properties of this quotient space: it has constant sectional curvature equal to 1, the Riemannian exponential...

In this paper, an algorithm for the coupled simulation of circuit and piezoelectric laminate devices is presented. A finite element solver for piezoelectric laminates is included in the SPICE framework as a capacitor. The charge of this capacitor is a function of both the terminal voltage and the mechanical strain in the piezoelectric material. The coupled simulator allows simulation of novel m...

Increasing numbers of analog components in today’s systems necessitate system level test composition methods that utilize onchip capabilities rather than solely relying on costly DFT approaches. We outline a tolerance analysis methodology for test signal propagation to be utilized in hierarchical test generation for analog circuits. A detailed justification of this proposed novel tolerance anal...