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<h3 class="likesectionHead"><a
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class="cmr-12">Abstract</span></h3>
<a
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<!--l. 5--><p class="noindent" ><span
class="cmcsc-10x-x-120">MLD2P4 (M<span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span><span
class="small-caps">i</span>L<span
class="small-caps">e</span><span
class="small-caps">v</span><span
class="small-caps">e</span><span
class="small-caps">l</span> D<span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">a</span><span
class="small-caps">i</span><span
class="small-caps">n</span> D<span
class="small-caps">e</span><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">p</span><span
class="small-caps">o</span><span
class="small-caps">s</span><span
class="small-caps">i</span><span
class="small-caps">t</span><span
class="small-caps">i</span><span
class="small-caps">o</span><span
class="small-caps">n</span> P<span
class="small-caps">a</span><span
class="small-caps">r</span><span
class="small-caps">a</span><span
class="small-caps">l</span><span
class="small-caps">l</span><span
class="small-caps">e</span><span
class="small-caps">l</span> P<span
class="small-caps">r</span><span
class="small-caps">e</span><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">n</span><span
class="small-caps">d</span><span
class="small-caps">i</span><span
class="small-caps">t</span><span
class="small-caps">i</span><span
class="small-caps">o</span><span
class="small-caps">n</span><span
class="small-caps">e</span><span
class="small-caps">r</span><span
class="small-caps">s</span></span>
<span
class="cmcsc-10x-x-120">P<span
class="small-caps">a</span><span
class="small-caps">c</span><span
class="small-caps">k</span><span
class="small-caps">a</span><span
class="small-caps">g</span><span
class="small-caps">e</span> <span
class="small-caps">b</span><span
class="small-caps">a</span><span
class="small-caps">s</span><span
class="small-caps">e</span><span
class="small-caps">d</span> <span
class="small-caps">o</span><span
class="small-caps">n</span> PSBLAS</span><span
class="cmr-12">) is a package of parallel algebraic multilevel</span>
<span
class="cmr-12">preconditioners. The first release of MLD2P4 made available multilevel additive and</span>
<span
class="cmr-12">hybrid Schwarz preconditioners, as well as one-level additive Schwarz preconditioners.</span>
<span
class="cmr-12">The package has been extended to include further multilevel cycles and smoothers</span>
<span
class="cmr-12">widely used in multigrid methods. In the multilevel case, a purely algebraic approach is</span>
<span
class="cmr-12">applied to generate coarse-level corrections, so that no geometric background is needed</span>
<span
class="cmr-12">concerning the matrix to be preconditioned. The matrix is assumed to be square, real</span>
<span
class="cmr-12">or complex.</span>
<!--l. 14--><p class="indent" > <span
class="cmr-12">MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in</span>
<span
class="cmr-12">the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms)</span>
<span
class="cmr-12">computational framework and can be used in conjuction with the Krylov solvers</span>
<span
class="cmr-12">available in this framework. MLD2P4 enables the user to easily specify different</span>
<span
class="cmr-12">features of an algebraic multilevel preconditioner, thus allowing to search for the “best”</span>
<span
class="cmr-12">preconditioner for the problem at hand.</span>
<!--l. 21--><p class="indent" > <span
class="cmr-12">The package employs object-oriented design techniques in Fortran</span><span
class="cmr-12"> 2003, with</span>
<span
class="cmr-12">interfaces to additional third party libraries such as MUMPS, UMFPACK, SuperLU,</span>
<span
class="cmr-12">and SuperLU</span><span
class="cmr-12">_Dist, which can be exploited in building multilevel preconditioners. The</span>
<span
class="cmr-12">parallel implementation is based on a Single Program Multiple Data (SPMD)</span>
<span
class="cmr-12">paradigm; the inter-process communication is based on MPI and is managed mainly</span>
<span
class="cmr-12">through PSBLAS.</span>
<!--l. 29--><p class="indent" > <span
class="cmr-12">This guide provides a brief description of the functionalities and the user interface</span>
<span
class="cmr-12">of MLD2P4.</span>
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