https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Gierden_et_al_2022a Gierden et al 2022a - Revision history 2026-04-20T20:34:12Z Revision history for this page on the wiki MediaWiki 1.27.0-wmf.10 https://www.scipedia.com/wd/index.php?title=Gierden_et_al_2022a&diff=262510&oldid=prev Move page script: Move page script moved page Gierden et al 1970a to Gierden et al 2022a 2022-11-25T15:06:15Z <p>Move page script moved page <a href="/public/Gierden_et_al_1970a" class="mw-redirect" title="Gierden et al 1970a">Gierden et al 1970a</a> to <a href="/public/Gierden_et_al_2022a" title="Gierden et al 2022a">Gierden et al 2022a</a></p> <table class="diff diff-contentalign-left" data-mw="interface"> <tr style='vertical-align: top;' lang='en'> <td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 15:06, 25 November 2022</td> </tr><tr><td colspan='2' style='text-align: center;' lang='en'><div class="mw-diff-empty">(No difference)</div> </td></tr></table> Move page script https://www.scipedia.com/wd/index.php?title=Gierden_et_al_2022a&diff=261476&oldid=prev JSanchez: JSanchez moved page Draft Sanchez Pinedo 378326049 to Gierden et al 1970a 2022-11-23T09:40:45Z <p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_378326049" class="mw-redirect" title="Draft Sanchez Pinedo 378326049">Draft Sanchez Pinedo 378326049</a> to <a href="/public/Gierden_et_al_1970a" class="mw-redirect" title="Gierden et al 1970a">Gierden et al 1970a</a></p> <table class="diff diff-contentalign-left" data-mw="interface"> <tr style='vertical-align: top;' lang='en'> <td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 09:40, 23 November 2022</td> </tr><tr><td colspan='2' style='text-align: center;' lang='en'><div class="mw-diff-empty">(No difference)</div> </td></tr></table> JSanchez https://www.scipedia.com/wd/index.php?title=Gierden_et_al_2022a&diff=261475&oldid=prev JSanchez at 09:40, 23 November 2022 2022-11-23T09:40:40Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 09:40, 23 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6" >Line 6:</td> <td colspan="2" class="diff-lineno">Line 6:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Abstract ==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Abstract ==</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;pdf&gt;Media:Draft_Sanchez Pinedo_3783260491326_abstract.pdf&lt;/pdf&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;pdf&gt;Media:Draft_Sanchez Pinedo_3783260491326_abstract.pdf&lt;/pdf&gt;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Full Paper ==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;pdf&gt;Media:Draft_Sanchez Pinedo_3783260491326_paper.pdf&lt;/pdf&gt;</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:261473:newid:261475 --> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Gierden_et_al_2022a&diff=261473&oldid=prev JSanchez at 09:40, 23 November 2022 2022-11-23T09:40:39Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 09:40, 23 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger equation. Incorporating a model order reduction technique based on calculations with a reduced set of Fourier modes, the computational cost of this algorithm can be decreased. It was shown that the accuracy of this model order reduction technique strongly depends on the choice of Fourier modes by considering a geometrically adapted rather than a fixed sampling pattern to define the reduced set of Fourier modes. Since it is difficult to define a geometrically adapted sampling pattern for complex microstructures, additionally a strain-based sampling pattern was introduced. The accuracy and adaptability of this strain-based reduced set of Fourier modes is shown by incorporating a polycrystalline microstructure.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger equation. Incorporating a model order reduction technique based on calculations with a reduced set of Fourier modes, the computational cost of this algorithm can be decreased. It was shown that the accuracy of this model order reduction technique strongly depends on the choice of Fourier modes by considering a geometrically adapted rather than a fixed sampling pattern to define the reduced set of Fourier modes. Since it is difficult to define a geometrically adapted sampling pattern for complex microstructures, additionally a strain-based sampling pattern was introduced. The accuracy and adaptability of this strain-based reduced set of Fourier modes is shown by incorporating a polycrystalline microstructure.</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Abstract ==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;pdf&gt;Media:Draft_Sanchez Pinedo_3783260491326_abstract.pdf&lt;/pdf&gt;</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:261471:newid:261473 --> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Gierden_et_al_2022a&diff=261471&oldid=prev JSanchez at 09:40, 23 November 2022 2022-11-23T09:40:37Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 09:40, 23 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Summary==</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger equation. Incorporating a model order reduction technique based on calculations with a reduced set of Fourier modes, the computational cost of this algorithm can be decreased. It was shown that the accuracy of this model order reduction technique strongly depends on the choice of Fourier modes by considering a geometrically adapted rather than a fixed sampling pattern to define the reduced set of Fourier modes. Since it is difficult to define a geometrically adapted sampling pattern for complex microstructures, additionally a strain-based sampling pattern was introduced. The accuracy and adaptability of this strain-based reduced set of Fourier modes is shown by incorporating a polycrystalline microstructure.</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:261470:newid:261471 --> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Gierden_et_al_2022a&diff=261470&oldid=prev JSanchez: Created blank page 2022-11-23T09:40:35Z <p>Created blank page</p> <p><b>New page</b></p><div></div> JSanchez