Francesco P. Andriulli

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Abstract. This paper deals with a multiresolution approach to the finite-element solution of the Electric Field Integral Equation (EFIE) formulation of the boundary value problem for Maxwell equations. After defining a multiresolution set of discretized spaces, each of them is first separated into solenoidal and non-solenoidal complementary spaces. The(More)
The Magnetic Field Integral Equation (MFIE) is a widely used integral equation for the solution of electromagnetic scattering problems involving perfectly conducting objects. It is usually discretized by means of RWG functions as both basis and test functions. This discretization of the MFIE is well-known for its good condition number. However, it is(More)
This paper presents a new set of hierarchical vector elements of arbitrarily high polynomial order constructed by using new orthogonal scalar polynomials. These novel vector elements, with respect to existing ones, provide better conditioned system matrices in finite methods applications. The scalar polynomials are subdivided into edge-, face-, and(More)
We introduce a novel combined field integral equation that does not suffer from internal resonances and solves several drawbacks of existing resonance-free formulations. The new equation is obtained by combining a regularized electric type operator with a new magnetic type operator that exhibits uniform frequency scaling when acting on, or being tested(More)
In this paper, a novel volume integral equation for solving the Electroencephalography forward problem is presented. Differently from other integral equation methods standardly used for the same purpose, the new formulation can handle inhomogeneous and fully anisotropic realistic head models. The new equation is obtained by a suitable use of Green's(More)
This paper presents a stabilization of a Radio-Frequency Quadrupole simulation based on the quasi-Helmholtz projectors. A boundary element method applied to this case undergoes a low-frequency breakdown i.e the associated system of equations becomes increasingly ill-conditioned for decreasing frequencies. This in practice implies that the convergence of(More)
Razor blade testing schemes have been proposed in the past for both the EFIE and MFIE. The regularity of these testing functions is, strictly speaking, not sufficient for the discretization to be conforming. However, as will be shown in the contribution, it does yield physical solution currents at low frequencies. This is similar to the low-frequency(More)
The time domain PMCHWT equation models transient scattering by piecewise homogeneous dielectrics. After discretization, it can be solved using the marching-on-in-time algorithm. Unfortunately, the PMCHWT equation suffers from DC instability: it supports constant in time regime solutions. Upon discretization, the corresponding poles of the system response(More)
All known integral equation techniques for simulating scattering and radiation from arbitrarily shaped, perfect electrically conducting objects suffer from one or more of the following shortcomings: (i) they give rise to ill-conditioned systems when the frequency is low (ii) and/or when the discretization density is high, (iii) their applicability is(More)
Objectives, expectations and difficulties associated to the use of multi-resolution (MR) constructs in integral equation, method of moments (MoM) are reviewed and put in a contemporary perspective. A MR approach is presented that can be applied to any mesh without any constrain on the structure topology. The so-obtained MR basis positively affects the(More)