Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems

<table><tr><td><table class="algorithm" id="alg5"><tr><td colspan="2"><svg height="12.4375" id="M166" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 36.262501 12.4375" width="36.262501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr><tr><td colspan="2"><svg height="16.075001" id="M167" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 89.974998 16.075001" width="89.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,20.838,11.788)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,35.541,11.788)"><path d="M17 676h194v-259q53 56 122 56q82 0 135 -65t53 -169q0 -113 -63 -183t-163 -70q-71 0 -132 57l-79 -56h-12v607q0 30 -10 40.5t-45 17.5v24zM211 360v-263q0 -36 19 -57.5t50 -21.5q94 0 94 203q0 198 -93 198q-47 0 -70 -59z" id="x1D41B"></path></g><g transform="matrix(.017,-0,0,-.017,48.766,11.788)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,62.518,11.788)"><path d="M689 25v-25h-322v25l32 3q46 4 46 33q0 31 -46 136h-225l-13 -34q-31 -78 -31 -97q0 -36 81 -41v-25h-202v25q36 6 53 28q18 22 46 92l221 545h28l222 -522q36 -87 58 -117q21 -26 52 -26zM189 236h195l-101 243z" id="x1D400"></path></g><g transform="matrix(.017,-0,0,-.017,74.792,11.788)"><path d="M484 24v-24h-241v24q45 3 45 20q0 16 -33 64q-23 32 -42 63l-16 -20q-64 -76 -64 -103q0 -21 50 -24v-24h-169v24q27 1 49 19q20 16 64 74l43 56q8 9 11 14t11 14l-128 197q-15 23 -24 29.5t-28 9.5v24h250v-24q-47 -2 -47 -19q0 -22 58 -98q7 -8 13 -17l36 46
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<g transform="matrix(.012,-0,0,-.012,83.3,15.875)"><path d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1
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</svg> compute in high precision</td></tr><tr><td colspan="2"><svg height="16.075001" id="M168" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 62.037498 16.075001" width="62.037498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,19.887,15.875)"><path d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1
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<g transform="matrix(.012,-0,0,-.012,55.362,15.875)"><path d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1
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</svg> solve in low precision</td></tr><tr><td colspan="2"><svg height="12.675" id="M169" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 94.150002 12.675" width="94.150002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> correct in high precision</td></tr><tr><td colspan="2"><svg height="12.4375" id="M170" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 62.337502 12.4375" width="62.337502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> iterate until convergence in high precision</td></tr></table></td></tr></table>

Mixed precision strategy for linear equation solvers.

Mathematical Problems in Engineering

alg5

Algorithm 5

Algorithm 5: Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems 