Ifpack2 Templated Preconditioning Package
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Ifpack2_Details_Chebyshev_Weights.hpp
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/*
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//@HEADER
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// ***********************************************************************
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//
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// Ifpack2: Templated Object-Oriented Algebraic Preconditioner Package
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// Copyright (2009) Sandia Corporation
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//
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// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
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// license for use of this work by or on behalf of the U.S. Government.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// 1. Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// 2. Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// 3. Neither the name of the Corporation nor the names of the
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// contributors may be used to endorse or promote products derived from
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// this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
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// Questions? Contact Michael A. Heroux (maherou@sandia.gov)
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//
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// ***********************************************************************
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//@HEADER
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*/
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#ifndef IFPACK2_DETAILS_CHEBYSHEV_WEIGHTS_HPP
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#define IFPACK2_DETAILS_CHEBYSHEV_WEIGHTS_HPP
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#include <stdexcept>
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#include <vector>
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#include "Teuchos_StandardParameterEntryValidators.hpp"
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namespace
Ifpack2
{
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namespace
Details {
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template
<
typename
ScalarType>
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std::vector<ScalarType>
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optimalWeightsImpl
(
const
int
chebyOrder)
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{
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if
(chebyOrder == 0){
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return
{};
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}
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if
(chebyOrder == 1){
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return
{
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1.12500000000000,
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};
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}
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if
(chebyOrder == 2){
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return
{
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1.02387287570313,
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1.26408905371085,
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};
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}
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if
(chebyOrder == 3){
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return
{
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1.00842544782028,
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1.08867839208730,
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1.33753125909618,
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};
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}
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if
(chebyOrder == 4){
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return
{
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1.00391310427285,
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1.04035811188593,
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1.14863498546254,
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1.38268869241000,
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};
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}
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if
(chebyOrder == 5){
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return
{
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1.00212930146164,
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1.02173711549260,
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1.07872433192603,
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1.19810065292663,
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1.41322542791682,
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};
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}
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if
(chebyOrder == 6){
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return
{
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1.00128517255940,
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1.01304293035233,
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1.04678215124113,
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1.11616489419675,
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1.23829020218444,
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1.43524297106744,
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};
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}
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if
(chebyOrder == 7){
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return
{
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1.00083464397912,
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1.00843949430122,
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1.03008707768713,
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1.07408384092003,
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1.15036186707366,
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1.27116474046139,
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1.45186658649364,
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};
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}
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if
(chebyOrder == 8){
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return
{
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1.00057246631197,
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1.00577427662415,
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1.02050187922941,
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1.05019803444565,
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1.10115572984941,
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1.18086042806856,
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1.29838585382576,
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1.46486073151099,
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};
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}
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if
(chebyOrder == 9){
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return
{
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1.00040960072832,
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1.00412439506106,
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1.01460212148266,
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1.03561113626671,
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1.07139972529194,
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1.12688273710962,
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1.20785219140729,
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1.32121930716746,
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1.47529642820699,
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};
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}
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if
(chebyOrder == 10){
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return
{
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1.00030312229652,
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1.00304840660796,
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1.01077022715387,
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1.02619011597640,
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1.05231724933755,
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1.09255743207549,
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1.15083376663972,
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1.23172250870894,
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1.34060802024460,
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1.48386124407011,
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};
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}
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if
(chebyOrder == 11){
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return
{
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1.00023058595209,
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1.00231675024028,
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1.00817245396304,
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1.01982986566342,
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1.03950210235324,
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1.06965042700541,
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1.11305754295742,
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1.17290876275564,
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1.25288300576792,
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1.35725579919519,
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1.49101672564139,
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};
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}
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if
(chebyOrder == 12){
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return
{
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1.00017947200828,
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1.00180189139619,
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1.00634861907307,
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1.01537864566306,
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1.03056942830760,
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1.05376019693943,
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1.08699862592072,
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1.13259183097913,
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1.19316273358172,
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1.27171293675110,
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1.37169337969799,
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1.49708418575562,
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};
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}
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if
(chebyOrder == 13){
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return
{
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1.00014241921559,
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1.00142906932629,
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1.00503028986298,
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1.01216910518495,
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1.02414874342792,
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1.04238158880820,
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1.06842008128700,
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1.10399010936759,
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1.15102748242645,
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1.21171811910125,
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1.28854264865128,
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1.38432619380991,
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1.50229418757368,
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};
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}
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if
(chebyOrder == 14){
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return
{
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1.00011490538261,
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1.00115246376914,
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1.00405357333264,
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1.00979590573153,
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1.01941300472994,
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1.03401425035436,
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1.05480599606629,
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1.08311420301813,
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1.12040891660892,
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1.16833095655446,
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1.22872122288238,
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1.30365305707817,
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1.39546814053678,
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1.50681646209583,
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};
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}
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if
(chebyOrder == 15){
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return
{
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1.00009404750752,
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1.00094291696343,
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1.00331449056444,
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1.00800294833816,
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1.01584236259140,
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1.02772083317705,
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1.04459535422831,
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1.06750761206125,
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1.09760092545889,
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1.13613855366157,
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1.18452361426236,
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1.24432087304475,
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1.31728069083392,
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1.40536543893560,
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1.51077872501845,
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};
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}
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if
(chebyOrder == 16){
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return
{
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1.00007794828179,
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1.00078126847253,
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1.00274487974401,
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1.00662291017015,
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1.01309858836971,
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1.02289448329337,
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1.03678321409983,
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1.05559875719896,
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1.08024848405560,
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1.11172607131497,
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1.15112543431072,
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1.19965584614973,
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1.25865841744946,
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1.32962412656664,
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1.41421360695576,
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1.51427891730346,
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};
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}
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TEUCHOS_TEST_FOR_EXCEPTION(
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true
, std::runtime_error,
"Ifpack2::Details::optimalWeightsImpl::"
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"Requested Chebyshev order exceeds maximum of 16."
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);
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}
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}
// namespace Details
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}
// namespace Ifpack2
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#endif
// IFPACK2_DETAILS_CHEBYSHEV_WEIGHTS_HPP
Ifpack2::Details::optimalWeightsImpl
std::vector< ScalarType > optimalWeightsImpl(const int chebyOrder)
Generate optimal weights for using the fourth kind Chebyshev polynomials see: https://arxiv....
Definition
Ifpack2_Details_Chebyshev_Weights.hpp:75
Ifpack2
Preconditioners and smoothers for Tpetra sparse matrices.
Definition
Ifpack2_AdditiveSchwarz_decl.hpp:74
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