Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical  Boundary Conditions

<table>Influence of the overlap size on the convergence rate of the SWR algorithm. Top: with <svg height="11.6375" id="M101" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 54.474998 11.6375" width="54.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> the solution generated by the SWR algorithm after 2, 4, and 6 iterations; bottom: the similar information for <svg height="11.6375" id="M102" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 54.474998 11.6375" width="54.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t98.5 -62.5q61 48 61 124q0 59 -29.5 90t-69.5 31zM248 20q46 0 76.5 33.5t30.5 89.5q0 50 -39 85.5t-110 71.5q-81 -54 -81 -137q0 -67 35.5 -105t87.5 -38z" id="x38"></path></g><g transform="matrix(.017,-0,0,-.017,34.009,11.362)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g><g transform="matrix(.017,-0,0,-.017,44.905,11.362)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g>
</svg>.</table>

Abstract and Applied Analysis

fig1

Figure 1

Figure 1: Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical  Boundary Conditions 