Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations

<table class="table-group" id="tab13"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">Spatial modes</td><td class="align_center">Execution time (sec)</td><td class="align_center">Average % error</td><td class="align_center">F-norm % error</td><td class="align_center">Inf-norm % error</td><td class="align_center">Reduced memory as % of original</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">2</td><td class="align_center">194.99</td><td class="align_center">9.1723</td><td class="align_center">6.6620</td><td class="align_center">11.6826</td><td class="align_center">2.018655</td></tr><tr><td class="align_left">3</td><td class="align_center">637.07</td><td class="align_center">7.4423</td><td class="align_center">3.0774</td><td class="align_center">11.8072</td><td class="align_center">3.027982</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Densities of 3D reduced model built from all <svg height="11.439pt" id="M248" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 44.5435 11.439" width="44.5435pt" 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="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.051,0)"><path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.158,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.577,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.84,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,38.08,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"></path></g></svg> 2D reduced models.</div>

International Journal of Aerospace Engineering

tab13

Table 13

Table 13: Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations 