SaqarTvelos erovnuli samecniero fondi

volmiri a. (Wol’mir, A. ) 1. Shells on the flow fluid and gas. Problems of Hydro-elasticity, Moscow, 1981, (Russian)

ianenko n.n. (Ianenko, N.N.) 1. Fractional steps method of solving for multi-dimensional problems of mathematical physics. Novosibirsk, Nauka (1967)

iegeri v., mikeliki a. (Jäger, W., Mikelic, A. ) 1. On the Boundary Conditions at the Contact Interface Between a Porous Medium and a Free Fluid. IWR, University of Heidelberg, Preprint 98-58, Heidelberg, 1994

ienseni s. (Jensen S.) 1. Adaptive dimensional reduction and divergence stability, Math. Model. 8 (1996), 9, 44-52.

leveki r.J. (LeVeque, R.J.) 1. Balancing source term and flux gradients in high resolution Godunov methods: The quasi-steady state wave propagation algorithm, J. Comput. Phys. 146 (1998) 346–365.

marCuki g. (Marchuk G.) 1. Split methods. Nauka, Moscow, (1988)

maxoveri e.v. (Makhover, E.V. ) 1. Bending of a plate of variable thickness with a cusped edge. Scientific Notes of Leningrad State Ped. Institute, 17, 2(1957), 28-39. (Russian)

mixlini s.g. (Mikhlin, S.G. ) 1. Variational Methods in Mathematical Physics. Nauka, Moscow, 1970. (Russian)

meunargia T. (Meunargia, T.) 1. On nonlinear and nonshallow shells. Bulletin of TICMI, (1998), 46-49. (for the electronic version: http://www.viam.hepi.edu.ge/others/TICMI)

pertami b., simeoni c. (Perthame, B., Simeoni C.) 1. A kinetic scheme for the Saint–Venant system with a source term, ENS preprint 01-13, 2001.

pismani d., reCfordi h. (Peaceman, D. and Rachford, H.) 1. The numerical solution of parabolic and elliptic differential equations. SIAM 3 (1955) 2841

samarski a. (Samarskii, A.) 1. On an economical difference method for the solution of a multi-dimensional parabolic equation in an arbitrary region. SSSR Comput. Math. Math. Phys. 2 (1962) 787-811

sanCes-palensia e. (Sanchez-Palensia, E.) 1. Non-homogeneous media and vibration theory. Moscow, Mir 1984, (Russian)

temami r. (Temam, R.) 1. Sur la stabilite et la convergence de la methode des pas fractionnaires. Ann. Mat. Pura Appl. 4 (1968) 191-379

fogeliusi m., babuSka i. (Vogelius, M., Babuška, I.) 1-3. On a dimensional reduction method, I. The optimal selection of basis functions; II. Some approximation-theoretic results; III. A posteriori error estimation and an adaptive approach, Math. of Comput. 37 (1981), 155, 31-46; 37 (1981), 155, 47-68; 37 (1981), 156, 361-384.

Svabi k. (Schwab, C.) 1. A-posteriori modeling error estimation for hierarchic Plate Models. Numerische Mathematik, 74(1996), 221-259

CinCalaZe n. (Chinchaladze, N. ) 1. Bending of an isotropic cusped elastic plates under action of an incompressible fluid. Reports of Seminar of . I. Vekua Institute of Applied Mathematics of Tbilisi State University, vol. 28 (2002), pp.31-39

2. Cylindrical vibration of an elastic cusped plate under action of an incompressible fluid in case of N=0 approximation of I.Vekua's hierarchical models. Complex Variables. Vol. 50, No. 7-11, 2005 (with R. Gilbert)

3. Vibration of the plate with two cusped edges. Proceedings of I.Vekua Institute of Applied Mathematics of Tbilisi State University, vol. 52 (2002),30-48

CinCalaZe n., jaiani g. (Chinchaladze, N., Jaiani, G. ) 1. On a cusped elastic solid-fluid interaction problem. Applied Mathematics and Informatics, vol. 6, No.2 (2001), 25-64

2. On a cylindrical bending of a plate with two cusped edges under action of an ideal fluid. Bull. TICMI, vol. 2 (1998), 30-34 for the electronic version see: http://www.viam.hepi.edu.ge/others/ticmi

3. On Big Deflections of Cusped Plates, Bull.TICMI, Vol. 9, 6-13, 2005 for the electronic version see: http://www.viam.hepi.edu.ge/others/ticmi

xvolesi a.r. (Khvoles, A.R. ) 1. The general representation for solutions of equilibrium equations of prismatic shell with variable thickness. Seminar of the Institute of Applied Mathematics of Tbilisi State University, Annot. of Reports, 5(1971), 19-21. (Russian)

xoma i. (Khoma, I. ) 1. The Generalized Theory of Anisotropic Shells. Naukova Dumka, Kiev 1986. (Russian)

jaiani g. (Jaiani, G. ) 1. On a physical interpretation of Fichera’s function, Acad. Naz. dei Lincei, Rend. della Sc. Fis. Mat. e Nat., S. 8, 68, fasc.5(1980), 426-435.

2. Solution of Some Problems for a Degenerate Elliptic Equation of Higher Order and Their Applications to Prismatic Shells. Tbilisi University Press, 1982. (Russian)

3. Theory of Cusped Euler-Bernoulli Beams and Kirchoff-Love Plates, Lecture Notes of TICMI, Vol.3, 2002 (for the electronic version see: http://www.viam.hepi.edu.ge/others/ticmi)

4. Elastic Bodies with Non-smooth Boundaries – Cusped Plates and Shells, ZAAM-Zeitschrift fuer Angewandte Mathematik und Mechanik, Vol.76, Supplement 2, pp.117-120, 1996

5. On a mathematical model of bars with variable rectangular cross-sections, ZAMMZeitschrift fuer Angewandte Mathematik und Mechanik, Vol.81, 3 (2001), 147-173

6. Relation of Hierarchical Models of Cusped Elastic Plates and Beams to the Three-dimensional Models, Reports of the Seminar of I.Vekua Institute of Applied Mathematics, Vol. 28, 40-51, 2002

jaiani g., xaribegaSvili s., natroSvili d., vendlandi v.l. (Jaiani G., Kharibegashvili S., Natroshvili D., Wendland W.L.) 1. Two-dimensional Hierarchical Models for Prismatic Shells with Thickness Vanishing at the Boundary, Journal of Elasticity, Vol. 77, No. 2, pp. 95-122
2. mosalodneli Sedegebi da maTi gamoyeneba

kvleva ganekuTvneba fundamentur kvlevaTa kategorias. agebuli da gamokvleuli iqneba Txeli drekadi da Txevadi fenebisagan Semdgari sxeulebis erTiani ierarqiuli modelebi, rac garkveuli azriT erTian sistemaSi moiyvans da gadafaravs aseTi tipis obieqtebisaTvis aqamde Catarebul gamokvlevebs. myari da Txevadi nawilebisagan Semdgari sxeulebisaTvis erTiani ierarqiuli modelebis ageba iqneba swored axali xedva. cvalebadi geometriis, maT Soris wamaxvilebuli, mravalfenovani drekadi da Txevadi nawilebis ganxilva mogvcems sanapiro zolis midamoSi mimdinare procesebis ramdenadme realurTan miaxloebul maTematikuri aRwerisa da misi simulirebis saSualebas. kompiuteruli eqsperimentebi momavalSi saSualebas mogvcems SemuSavebul iqnas rekomendaciebi sanapiro zolis dacvis TvalsazrisiT.

2.1. mdgradi ganviTarebisaken gadasvlis gegma.

Seiqmneba programuli produqti, romelic sanapiro zolis midamoSi myar da Txevad garemoTa urTierTqmedebis Sedegad gamowveuli procesebis kompiuteruli simulirebis saSualebas mogvcems, ramac momavalSi SeiZleba dRis wesrigidan moxsnas am mimarTulebiT realuri ZviradRirebuli eqsperimentebis Catareba. aseTi produqtis potenciuri momxmarebeli SeiZleba iyos nebismieri organizacia, romelic zrunavs sanapiro zolis dacvaze. dainteresebuli organizaciebis arsebobis SemTxvevaSi, proeqtis Sedegebze dayrdnobiT, iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universitetis i. vekuas saxelobis gamoeyenebiTi maTematikis instituti (Tsu gmi) SesZlebs dakveTis saxiT Seasrulos damatebiTi samecniero-kvleviTi samuSaoebi da gasces saTanado rekomendaciebi, rac xels Seuwyobs damkveTi organizaciis winaSe mdgari praqtikuli saxis problemebis gadaWras.

miRebuli mecnieruli Sedegebi inglisur enaze anonsirebuli an srulad gamoqveynebuli iqneba Tsu gmi-s bazaze gamomaval saerTaSoriso JurnalebSi Applied Mathematics, Informatics and Mechanics (ISSN 1512-0074), Bulletin of TICMI (ISSN 1512-0082), Lecture Notes of TICMI (ISSN 1512-0511), institutis SromebSi (ISSN 1512-004X), seminaris moxsenebebSi (ISSN 1512-0058), da seminaris gafarToebuli sxdomebis moxsenebebSi (ISSN 1512-0066), romlebic gacvlis wesiT igzavneba msoflios umniSvnelovanes biblioTekebSi da samecniero centrebSi. garda amisa nawili Sedegebisa gaigzavneba sxva saerTaSoriso JurnalebSi gamosaqveyneblad. proeqtis dasrulebis Semdeg ki momzaddeba monografia miRebuli da gamoqveynebuli Sedegebis gadamuSavebis safuZvelze.

programuli produqti registrirebuli iqneba saTanado fondSi.

3. saqmianobis aRwera kvartalurad

yovelkvireul seminarze mosmenili iqneba monawileTa informacia maT mier gaweul samuSaos Taobaze an samecniero moxseneba.

Tsu i. vekuas saxelobis gamoyenebiTi maTematikis institutis saitze gaixsneba proeqtis veb-gverdi operatiuli informaciiT proeqtze muSaobis Taobaze, kerZod, anonsirebuli iqneba seminaris moxsenebebis Temebi.
I kvartali

amocana 1

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos wrfivi ierarqiuli modelebi	iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti (i. vekuas saxelobis gamoyenebiTi maTematikis instituti)	agebuli iqneba ierarqiuli mo­delebi variaciuli modgomis gamoyenebiT.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari

amocana 2

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos arawrfivi ierarqiuli modelebi sawyisi miaxloebebisaTvis	iv. javaxiSvilis saxelo­bis Tbilisis saxelmwifo uni­v­e­­rsiteti (i. vekuas sa­­x­e­l­o­bis gamoyenebiTi maT­ema­tikis instituti)	proeqciuli meTodebiT ageb­ul iqneba ierarqiuli araw­rfivi modelebis N=0,1,2 mia­x­loebebi, rodesac piriT zedapirebze cnobilia Zabvis veqtoris kom­ponentebi
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari

amocana 3

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
deformadi myari da Txevadi nawilebisagan Semdgari garemos ierarqiuli modelebis gantolebebis ricxviTi amoxsnis algoriTmebis ageba da gamokvleva	iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti (i. vekuas saxelobis gamoyenebiTi maTematikis instituti)	a) ganxiluli iqneba defor­ma­di myari da Txevadi nawile­bisagan Semdgari garemos iera­r­qiuli modelebisaTvis N=0,1 miax­loe­ba (dinamika). Sesaba­mi­si gantolebebisaTvis ganxi­luli iqneba naxevraddis­kre­tu­li sqemebi, romlebic mii­Reba droiTi cvladis mixed­viT warmoebulebis diskreti­za­ciiT da sivrciTi cvla­de­bis mixedviT warmoebulebis ga­saSualoebiT. gamokvleuli iqneba am sqemebis mdgradoba. b) marCxi wylis gantole­be­bi­saTvis agebuli iqneba maRali sizustis mqone sasrul mocu­lo­baTa wonasworuli tipis sqe­mebi. gamoyvanili iqneba sqe­mis zogierTi Tviseba.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari

II kvartali

amocana 1

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos wrfivi ierarqiuli modelebi	iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti (i. vekuas saxelobis gamoyenebiTi maTematikis instituti)	agebuli ierarqiuli modele­bi­saTvis gamokvleuli iqneba varia­ciuli formulirebiT das­muli amocanis amonaxsnis arse­bobis da erTaderTobis da Sesabamisi samganzomi­le­biani amocanis zusti amonax­snisaken miswrafebis sakiTxi, ro­ca garemos mier dakavebuli samganzomilebiani are lip­Si­cu­ria da mis mTel sazRvarze gadaad­gilebebia mocemuli, xo­lo interfeisze mocemulia gadaadgilebis veqtorisa da Zab­vis tenzoris uwyvetad gadas­vlis pirobebi.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari

amocana 2

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos arawrfivi ierarqiuli modelebi sawyisi miaxloebebisaTvis	iv. javaxiSvilis saxelo­bis Tbilisis saxelmwifo uni­v­e­­rsiteti (i. vekuas sa­­x­e­l­o­bis gamoyenebiTi maT­ema­tikis instituti)	­ageb­ul iqneba ierarqiuli ara­­w­r­fivi modelebis N=0,1,2 mia­x­loebebi, ro­de­sac piriT ze­da­pirebis erT nawilze cno­bilia gadaadgilebis veq­t­o­ris komponentebi, xolo meo­reze - Zabvis veqtoris ko­m­­­ponentebi (gverdiT zeda­pir­ze sasazRvro pirobebi kla­sikuria). gamyof zeda­pir­ze (interfeisze) mocemulia uwyvetad gadabmis pirobebi.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari

amocana 3

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
deformadi myari da Txevadi nawilebisagan Semdgari garemos ierarqiuli modelebis gantolebebis ricxviTi amoxsnis algoriTmebis ageba da gamokvleva	iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti (i. vekuas saxelobis gamoyenebiTi maTematikis instituti)	a) wina etapze agebuli sqe­me­bi­saTvis miRebuli iqneba aprio­ruli Sefasebebi, saida­nac gamomdinareobs miaxloe­bi­Ti amonaxsnis krebadoba zus­ti amonaxsnisaken saTanado kla­sebSi. b) damtkicebuli iqneba sas­rul moculobaTa wonas­wo­ru­li sqemis kreba­do­ba modelur SemTxvevaSi.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari, publikacia

III kvartali

amocana 1

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos wrfivi ierarqiuli modelebi	iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti (i. vekuas saxelobis gamoyenebiTi maTematikis instituti)	agebuli ierarqiuli modele­bi­saTvis gamokvleuli iqneba va­riaciuli formulirebiT das­muli amocanis amonaxsnis arse­bobis da erTaderTobis da Sesabamisi samganzo­mi­le­bia­ni amocanis zusti amonaxsni­sa­ken miswrafebis sakiTxi, ro­ca garemos mier dakavebuli samganzomilebiani are lip­Sicu­ria, mis piriT zeda­pirebze Zabvebi, xolo gver­diT zedapirze gadaadgile­be­bia mocemuli. interfeisze moce­mulia gadaadgilebis veq­torisa da Zabvis tenzoris uwyvetad gadasvlis pirobebi.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari, publikacia

amocana 2

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos arawrfivi ierarqiuli modelebi sawyisi miaxloebebisaTvis	iv. javaxiSvilis saxelo­bis Tbilisis saxelmwifo uni­v­e­­rsiteti (i. vekuas sa­­x­e­l­o­bis gamoyenebiTi maT­ema­tikis instituti)	Seswavlil iqneba N=0,1 mia­x­loe­bebisa da fizikur hipo­te­zebze dayrdnobiT agebul modelebs Soris mimarTebis sakiTxi.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari, publikacia

amocana 3

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
deformadi myari da Txevadi nawilebisagan Semdgari garemos ierarqiuli modelebis gantolebebis ricxviTi amoxsnis algoriTmebis ageba da gamokvleva	iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti (i. vekuas saxelobis gamoyenebiTi maTematikis instituti)	a) deformadi myari da Txe­vadi nawilebisagan Semdgari ga­remos rxevis ierarqiuli mo­delebis (miaxloeba N=0, 1) Sesabamisi gantolebebisaTvis sawyis-sasazRvro amocana miiy­vaneba evoluciur amocanaze, ro­mlisTvisac eqsponen­cia­lu­ri gaxleCis safuZvelze age­bu­li iqneba maRali rigis sizus­tis dekompoziciis sqe­me­bi. b) Sedgenili iqneba prog­rama damuSavebuli wonas­wo­ruli tipis sasrul mo­cu­lobaTa sqemis safuZvelze. Ca­tar­deba testuri amocanebis gaT­vlebi da Tvlis Sedegebis analizi.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari

IV kvartali

amocana 1

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos wrfivi ierarqiuli modelebi	iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti (i. vekuas saxelobis gamoyenebiTi maTematikis instituti)	agebuli iqneba diferencialu­ri ierarqiuli modelebi. N=0,1 miaxloebebSi gamokveu­li iqneba drekadi myari da Txe­vad garemoTa harmoniuli rxevebi, maSinac, roca garemos mier dakavebuli samganzo­mi­le­biani are ara lipSicuria.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari, publikacia, sademonstracio dRe

amocana 2

amocanis dasaxeleba	monawile organizaciebi	miRebuli/mosalodneli Sedegebi
drekadi da Txevadi nawilebisagan Semdgari garemos arawrfivi ierarqiuli modelebi sawyisi miaxloebebisaTvis	iv. javaxiSvilis saxelo­bis Tbilisis saxelmwifo uni­v­e­­rsiteti (i. vekuas sa­­x­e­l­o­bis gamoyenebiTi maT­ema­tikis instituti)	N=0 miaxloebisaTvis dasmuli sawyis-sasazRvro amocanis amoxsnis meTodebis damuSaveba.
angariSgebis masalebis nusxa (dasaxuli amocanis Sesrulebis amsaxveli masala)
angariSi, seminari, publikacia, sademonstracio dRe