An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems

<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 class="align_left">Strategy</td><td class="align_center"><span style="width: 11.0475ptpx;"><svg height="8.8423pt" id="M66" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 11.0475 8.8423" width="11.0475pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839" xpluscharwidth="10.907"></glyph.data></g></svg></span></td><td class="align_center">Var</td><td class="align_center">Eq</td><td class="align_center">Iter</td><td class="align_center">Accuracy</td><td class="align_center">CPU(s)</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">ESM</td><td class="align_center">104</td><td class="align_center">36</td><td class="align_center">31</td><td class="align_center">8</td><td class="align_center"><span style="width: 31.4992ptpx;"><svg height="8.69875pt" id="M67" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 31.4992 8.69875" width="31.4992pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="6.24"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="414" vert-adv-y="414" xpluscharwidth="11.622"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.528,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587" xpluscharwidth="22.159"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,25.064,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="31.304000000000002"></glyph.data></g></svg></span></td><td class="align_center">67.277</td></tr><tr><td class="align_left">MFE</td><td class="align_center">8</td><td class="align_center">248</td><td class="align_center">217</td><td class="align_center">71</td><td class="align_center"><span style="width: 31.4992ptpx;"><svg height="8.69875pt" id="M68" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 31.4992 8.69875" width="31.4992pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="6.24"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="414" vert-adv-y="414" xpluscharwidth="11.622"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.528,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587" xpluscharwidth="22.159"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,25.064,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="31.304000000000002"></glyph.data></g></svg></span></td><td class="align_center">5.352</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems 