The paper presents the effectiveness of the parametric integral equation system (PIES) in solving 3D boundary problems defined by Navier-Lame equations on the example of the polygonal boundary and in comparison with the boundary element method (BEM). Analysis was performed using the commercial software “BEASY” which bases on the BEM method, whilst in the case of PIES using an authors software. ...

In this work we consider the solution of the linear systems arising from electromagentism applications by preconditioned Krylov subspace methods [3]. Simulation of electromagnetic wave propagation phenomena requires the numerical solution of Maxwell’s equations which it is often done by means of integral equation methods. The discretization of the integral equations with the boundary element me...

Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...

We consider the discretization in time of a parabolic equation, using a representation of the solution as an integral along a smooth curve in the complex left half plane. The integral is then evaluated to high accuracy by a quadrature rule. This reduces the problem to a finite set of elliptic equations, which may be solved in parallel. The procedure is combined with finite element discretizatio...

In this paper, the natural boundary element method (NBEM) for an anisotropic hyperbolic problem in an exterior elliptic domain is investigated. By the theory of the natural boundary reduction (NBR), the natural integral equation (NIE) and the Poisson integral formula of the problem considered are obtained, and the numerical method of the NIE is given. Finally, some numerical examples are presen...

We discuss the geometry of the Lagrangian quantization scheme based on (generalized) Schwinger-Dyson BRST symmetries. When a certain set of ghost fields are integrated out of the path integral, we recover the Batalin-Vilkovisky formalism, now extended to arbitrary functional measures for the classical fields. Keeping the ghosts reveals the crucial role played by a natural connection on the spac...

Purity of affine Springer fibers for GL4). — The affine Springer fiber corresponding to GL4 and regular semi-simple integral split element admits an affine paving, so its cohomology is “pure”.

A new method is proposed for the numerical evaluation of domain integrals in a 3D boundary element method. These integrals arise in the solution of the transient heat conduction problems, using a time-dependent boundary integral equation method named as pseudo-initial condition method. As the time-dependent kernel in the domain integral is close to singular when small time step is used, a strai...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with cor...

The greyscale imaging performance of a total 17 preclinical transducer/scanner combinations were measured over period 10 years. These comprised nine single element transducers and eight array with nominal central frequencies ranging between 15 55 MHz, from four commercially-available ultrasound scanners. Performance was assessed using figure merit, the resolution integral, measurements acquired...