Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

<table>Computational complexity of constructing <svg height="12.0625" id="M179" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 17.075001 12.0625" width="17.075001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,11.738)"><path d="M702 678l12 -14l-18 -14q-124 -96 -232 -310q25 10 62 21l53 18l33 43q101 126 187 195q88 70 135 70q57 0 57 -50q0 -78 -98 -145q-86 -58 -206 -105q-174 -251 -174 -334q0 -15 9.5 -25t24.5 -10q55 0 167 129l21 -13q-120 -146 -202 -146q-39 0 -63 24t-24 65
q0 101 104 262l-107 -41q-56 -110 -132 -193q-75 -82 -145 -109q-31 -11 -56 -11t-41 16.5t-16 43.5q0 129 283 247q17 29 20 33l22 36q1 2 9 13.5l14 20.5q18 28 59 77q34 39 87 86q-5 -1 -20 -1q-44 0 -124 44q-62 34 -102 34q-48 0 -82 -31q-34 -30 -34 -70q0 -44 22 -69
t66 -25q37 0 65 20.5t56 65.5l18 -9q-54 -107 -141 -107q-59 0 -93 34.5t-34 91.5q0 58 50 105q49 46 125 46q28 0 58 -11q35 -13 84 -38q59 -31 86 -31q42 0 80 19q16 9 42 28zM958 635q0 22 -24 22q-28 0 -86 -63q-56 -60 -128 -160q238 105 238 201zM307 241
q-110 -50 -165.5 -98t-55.5 -99q0 -24 24 -29q67 0 197 226z" id="x210B"></path></g>
</svg>-matrices by fixed discretization mesh density at 8 points per wavelength.</table>

International Journal of Antennas and Propagation

fig4

Figure 4

Figure 4: Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations 