Background of PML

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PML was orig­i­nal­ly de­vel­oped for elec­tro­mag­net­ic waves in sem­i­nal works by Bérenger and Chew in 1994, and fol­lowed up by ex­ten­sive in­ves­ti­ga­tion of elec­tro­mag­net­ic PMLs by nu­mer­ous re­searchers, as well as ex­ten­sions to oth­er fields such as elas­tic waves for seis­mic ap­pli­ca­tions.

Most of these for­mu­la­tions and im­ple­men­ta­tions used fi­nite-dif­fer­ence split-field meth­ods to im­ple­ment the PML, which had two dis­ad­van­tages: (i) the fi­nite-dif­fer­ence meth­ods could not be used eas­i­ly with fi­nite-el­e­ment mod­els for struc­tures, and (ii) the split-field for­mu­la­tion of­ten led to long-time in­sta­bil­i­ty.

These short­com­ings were rec­ti­fied for elas­tic PMLs by Ba­su and Chopra [2003, 2004, 2009] by de­vel­op­ing a dis­place­ment-based fi­nite-el­e­ment im­ple­men­ta­tion that al­lowed ex­plic­it analy­sis, thus en­abling re­al­is­tic analy­sis of three-di­men­sion­al soil-struc­ture sys­tems.