Subdomain Precise Integration Method for Periodic Structures

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td align="left"> </td><td align="center">SPIM <svg height="13.2498pt" id="M260" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 38.2674 13.2498" width="38.2674pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,4.688,0)"><path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 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192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,33.366,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg></td><td align="center" colspan="2">Newmark</td><td align="center">ODE45</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td align="left">Order</td><td align="center">4</td><td align="center">6</td><td align="center">8</td><td align="center" colspan="2">2</td><td align="center">—</td></tr><tr><td align="left"><svg height="9.7821pt" id="M263" style="vertical-align:-3.57194pt" version="1.1" viewbox="-0.0498162 -6.21016 6.81751 9.7821" width="6.81751pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="494" vert-adv-y="494"></glyph.data></g></svg> (s)</td><td align="center"><span style="width: 24.1049ptpx;"><svg height="12.1292pt" id="M264" style="vertical-align:-0.2129002pt" version="1.1" viewbox="-0.0498162 -11.9163 24.1049 12.1292" width="24.1049pt" 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vert-adv-y="487"></glyph.data></g></svg></span></td><td align="center">—</td></tr><tr><td align="left">CPU times (s)</td><td align="center">68</td><td align="center">169</td><td align="center">321</td><td align="center">291</td><td align="center">4779</td><td align="center">2338</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Comparison of CPU times for Example <a href="https://static.hindawi.com/articles/sv/volume-2014/657589/figures/#ex2">2</a>.

Shock and Vibration

Subdomain Precise Integration Method for Periodic Structures

Table 2