Francesco P. Andriulli

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This paper deals with a multiresolution approach to the finite-element solution of the Electric Field Integral Equation (EF IE) 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 possibility(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)
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)
With the advancement of technology, modern equipment involves new functionalities that require complex media (e.g., anisotropic dispersive media such as ferrite, lossy dielectrics, or graphene) for a variety of applications. This imposes the necessity to extend simulation techniques capable of solving Maxwell’s equations in such media. However, as(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)
We present a new preconditioner for the combined field integral equation (CFIE) that gives rise to a Hermitian, positive definite system of linear equations. Differently from other Calderón strategies, this scheme necessitates a standard discretization of the electric field integral equation (EFIE) with Rao-Wilton-Glisson (RWG) basis functions(More)
This work presents a novel analysis of Loop-Star and Loop-Tree quasi-Helmholtz decompositions. The spectral properties of Loop, Star, and Tree functions are investigated and linked to the conditioning of Helmholtz decomposed Electric, Magnetic, and Calderón Preconditioned Integral Equations. The analysis will explain and quantify the difference in(More)
Several preconditioning techniques have been developed to control the condition number of the linear system matrices arising from the majority of the integral formulations for electromagnetics problems. The performance of these techniques is usually assessed in two regimes: (i) the case where the number of unknowns is kept constant and the frequency(More)