Perfectly Matched Layer for the FDTD Solution of Wave-Structure Interaction in Spherical Coordinates Jasem Jamali Hamid Keivani Islamic Azad University – Kazeroon branch Abstract: - The perfectly matched layer, PML is a new technique developed for the simulation of free space with the finite difference time-domain (FDTD) method. This technique first was described by Berenger for Cartesian coordinate. This paper provides perfectly Matched Layer Equations for the FDTD method in Spherical Coordinate. Key-words: - Perfectly Matched Layer, Finite Difference Time Domain, Spherical Coordinates 1 Introduction The artificially imposed boundary at the edge of the simulation space needs to terminate in an absorbing layer to prevent spurious reflections from interfering with the outgoing wave. Because some of the scattering wave problems are in spherical coordinates, an absorbing boundary layer is spherically symmetric. That is the PML layer only needs to vary with the radius, r. So we can obtain equations that satisfy the PML region. These equations are obtained with details in section 2. 2 The PML Technique in Spherical Coordinate In order to form a PML, the following steps must be taken [1, 2]: 2.1 Resolve into the and components in the coupled Maxwell equations. φ H r H φ φθ H 2.2 Create FDTD equations from the revised Maxwell equations. 2.3 Modify the , , , and time constants to include exponential difference time advance [3]. a C b C a D b D 2.4 Calculate conductivity values for PML layers using the matching condition. Performing the first step involves splitting the magnetic field into one component due to r and one due to θ . Starting with the Maxwell equations given in spherical coordinates, and using a PML with electric and magnetic conductivities for r and θ respectively given by ( r σ , , ∗ r σ θ σ , ): ∗ θ σ ] ) (sin sin 1 [ 1 θ θ θ φθ θ σ μ φθ ∂ ⋅ ⋅ ∂ ⋅ + ⋅ ∗ − = ∂ ∂ r r E H t H (1) ] ) ( 1 [ 1 r E r r r H r t r H ∂ ⋅ ∂ ⋅ − ⋅ ∗ − = ∂ ∂ θ φ σ μ φ (2) ] )) ( (sin sin 1 [ 1 θ φθ φ θ θ θ σ ε ∂ ⋅ + ⋅ ∂ ⋅ + ⋅ − = ∂ ∂ r H r H r E t r E (3) ] )) ( ( 1 [ 1 r H r H r r E r t E ∂ + ∂ ⋅ − ⋅ − = ∂ ∂ φθ φ θ σ ε θ (4) These four Maxwell's equations can be converted into four FDTD equations in accordance with the second step given above. The results are as follows: Proceedings of the 10th WSEAS International Conference on COMMUNICATIONS, Vouliagmeni, Athens, Greece, July 10-12, 2006 (pp309-312)