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

<div>Evolution of the RAM for the computation of the electric field <svg height="8.73791pt" id="M208" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.68809 7.82449 8.73791" width="7.82449pt" 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="M539 178C521 133 503 101 484 80C461 55 424 49 376 49C339 49 302 51 284 59C264 68 260 92 260 137V305H325C410 305 422 302 435 229H478V436H435C422 366 409 361 325 361H260V565C260 599 263 600 303 600H353C406 600 433 594 450 576C466 559 478 527 487 492L531 498C526 561 522 632 521 650H41V608C113 602 123 597 123 513V137C123 55 113 49 28 42V0H546C554 29 575 122 581 169L539 178Z" id="g22-67"></path><glyph.data ascent="1041" descent="-369" horiz-adv-x="592" vert-adv-y="592"></glyph.data></g></svg> (a) and of the temperature <svg height="8.85534pt" id="M209" style="vertical-align:-0.04981041pt" version="1.1" viewbox="-0.0498162 -8.80553 8.51608 8.85534" width="8.51608pt" 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="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="673" vert-adv-y="673"></glyph.data></g></svg> (b) with strategies <svg height="11.8565pt" id="M210" style="vertical-align:-3.05097pt" version="1.1" viewbox="-0.0498162 -8.80553 15.4329 11.8565" width="15.4329pt" 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="M722 32C646 41 636 48 622 116L544 496L509 667L472 658L153 123C106 45 93 42 27 32L18 0H259L268 32C178 40 172 48 204 107L272 233H509C523 180 533 137 540 96C548 50 546 39 466 32L457 0H714L722 32ZM502 283H299L448 547H450L502 283Z" id="g50-66"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="740" vert-adv-y="740"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.348,3.001)"><path d="M389 0V32C297 37 291 46 291 118V635C234 612 176 595 109 583V556L161 554C203 551 207 548 207 497V118C207 46 201 37 110 32V0H389Z" id="g58-47"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, <svg height="11.8565pt" id="M211" style="vertical-align:-3.05097pt" version="1.1" viewbox="-0.0498162 -8.80553 15.4329 11.8565" width="15.4329pt" 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="M722 32C646 41 636 48 622 116L544 496L509 667L472 658L153 123C106 45 93 42 27 32L18 0H259L268 32C178 40 172 48 204 107L272 233H509C523 180 533 137 540 96C548 50 546 39 466 32L457 0H714L722 32ZM502 283H299L448 547H450L502 283Z" id="g50-66"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="740" vert-adv-y="740"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.348,3.001)"><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></svg>, and <svg height="11.9707pt" id="M212" style="vertical-align:-3.165171pt" version="1.1" viewbox="-0.0498162 -8.80553 15.4329 11.9707" width="15.4329pt" 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="M722 32C646 41 636 48 622 116L544 496L509 667L472 658L153 123C106 45 93 42 27 32L18 0H259L268 32C178 40 172 48 204 107L272 233H509C523 180 533 137 540 96C548 50 546 39 466 32L457 0H714L722 32ZM502 283H299L448 547H450L502 283Z" id="g50-66"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="740" vert-adv-y="740"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.348,3.001)"><path d="M290 377C321 398 342 415 358 430C379 451 389 475 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C113 529 154 573 208 573C263 573 303 542 303 482C303 409 233 371 141 341L149 308C165 313 190 319 215 319C272 319 341 284 341 193C342 97 293 43 222 43C162 43 123 71 96 94C89 101 80 101 70 94C61 87 47 73 46 60C44 48 49 36 62 23S118 -12 165 -12C238 -12 430 62 430 223C430 298 379 359 290 375V377Z" id="g58-49"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>.</div>

Advances in Mathematical Physics

fig5

Figure 5

Figure 5: Comparison of 3D Adaptive Remeshing Strategies for Finite Element Simulations of Electromagnetic Heating of Gold Nanoparticles 