Comparison of 3D Adaptive Remeshing Strategies for Finite Element Simulations of Electromagnetic Heating of Gold Nanoparticles

<div>Isosurfaces of the intensity of electric field (a) and temperature (b) associated with the initial mesh (<svg height="11.7619pt" id="M244" style="vertical-align:-3.16516pt" version="1.1" viewbox="-0.0498162 -8.59674 70.9726 11.7619" width="70.9726pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.231,3.001)"><path d="M245 635C92 635 37 457 37 312C37 148 92 -12 244 -12C395 -12 449 165 449 312C449 469 394 635 245 635ZM243 598C332 598 358 454 358 312C358 172 334 26 245 26C158 26 128 174 128 313S151 598 243 598Z" id="g58-46"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,18.853,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.471,0)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 317 408 376 408 465C408 569 328 635 237 635C178 635 131 610 100 575L42 494L67 471C94 511 138 565 205 565C277 565 321 518 321 435C321 348 259 269 195 195C146 136 89 82 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g58-48"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,36.802,0)"><path d="M253 635C142 635 71 555 71 471C71 400 113 353 178 316C143 295 107 268 91 252C70 231 46 202 46 157C46 50 132 -12 241 -12C329 -12 442 52 442 168C442 257 379 305 311 343C354 374 380 398 388 407C407 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 564 340 481C340 422 314 387 279 360C207 395 148 426 148 499C148 549 181 600 240 600ZM252 23C188 23 129 72 129 163C129 218 162 266 211 298C288 261 360 217 360 144C360 68 312 23 252 23Z" id="g58-54"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,43.133,0)"><path d="M247 635C116 635 39 517 39 421C39 315 112 237 221 237C240 237 258 241 281 253L349 289C314 140 205 42 60 19L66 -15C90 -15 153 -6 207 16C344 70 447 199 447 385C447 521 373 635 247 635ZM231 598C329 598 356 478 356 390C356 371 355 348 352 325C329 309 297 297 262 297C179 297 127 369 127 456C127 515 155 598 231 598Z" id="g58-55"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,51.741,0)"><path d="M141 347C170 480 264 541 327 570C364 587 403 598 436 605L429 641C389 634 339 622 300 609C192 569 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 379 397 272 397C252 397 231 391 208 380L141 347ZM231 338C323 338 366 257 366 174C366 107 339 27 263 27C180 27 129 123 129 244C129 268 130 291 135 310C158 323 192 338 231 338Z" id="g58-52"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,58.072,0)"><path d="M245 635C92 635 37 457 37 312C37 148 92 -12 244 -12C395 -12 449 165 449 312C449 469 394 635 245 635ZM243 598C332 598 358 454 358 312C358 172 334 26 245 26C158 26 128 174 128 313S151 598 243 598Z" id="g58-46"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,64.403,0)"><path d="M158 548H390L417 615L410 623H122L83 318C106 326 142 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C165 42 121 74 100 93C89 101 83 99 72 92C60 81 51 68 50 59C47 46 51 39 66 24C82 9 125 -12 172 -12C225 -11 291 15 346 59C409 108 437 166 437 226C437 309 370 397 242 397C214 397 170 382 133 369L158 548Z" id="g58-51"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> elements).</div>

Advances in Mathematical Physics

fig8

Figure 8

Figure 8: Comparison of 3D Adaptive Remeshing Strategies for Finite Element Simulations of Electromagnetic Heating of Gold Nanoparticles 